%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP181-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n005.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 16:53:36 EDT 2024

% Result   : Unsatisfiable 6.24s 6.43s
% Output   : Proof 6.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : GRP181-4 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.10/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sun May 26 17:45:24 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 6.24/6.43  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.oh4OzLmSnw/cvc5---1.0.5_1497.smt2
% 6.24/6.43  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.oh4OzLmSnw/cvc5---1.0.5_1497.smt2
% 6.68/6.90  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 6.68/6.90  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)))
% 6.68/6.90  (assume a2 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.68/6.90  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 6.68/6.90  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 6.68/6.90  (assume a5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound X Y) Z))))
% 6.68/6.90  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.least_upper_bound X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.least_upper_bound X Y) Z))))
% 6.68/6.90  (assume a7 (forall ((X $$unsorted)) (= (tptp.least_upper_bound X X) X)))
% 6.68/6.90  (assume a8 (forall ((X $$unsorted)) (= (tptp.greatest_lower_bound X X) X)))
% 6.68/6.90  (assume a9 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)))
% 6.68/6.90  (assume a10 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)))
% 6.68/6.90  (assume a11 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 6.68/6.90  (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 6.68/6.90  (assume a13 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.68/6.90  (assume a14 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.68/6.90  (assume a15 (= (tptp.inverse tptp.identity) tptp.identity))
% 6.68/6.90  (assume a16 (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)))
% 6.68/6.90  (assume a17 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.68/6.90  (assume a18 (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)))
% 6.68/6.90  (assume a19 (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)))
% 6.68/6.90  (assume a20 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.68/6.90  (assume a21 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.68/6.90  (assume a22 (not (= tptp.a tptp.b)))
% 6.68/6.90  (step t1 (cl (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (not (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule and_neg)
% 6.68/6.90  (step t2 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule implies_neg1)
% 6.68/6.90  (anchor :step t3)
% 6.68/6.90  (assume t3.a0 (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)))
% 6.68/6.90  (assume t3.a1 (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)))
% 6.68/6.90  (assume t3.a2 (= tptp.identity (tptp.inverse tptp.identity)))
% 6.68/6.90  (assume t3.a3 (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))
% 6.68/6.90  (assume t3.a4 (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)))
% 6.68/6.90  (assume t3.a5 (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))
% 6.68/6.90  (assume t3.a6 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))))
% 6.68/6.90  (assume t3.a7 (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.a8 (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.a9 (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.a10 (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.a11 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 6.68/6.90  (assume t3.a12 (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)))
% 6.68/6.90  (assume t3.a13 (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))
% 6.68/6.90  (assume t3.a14 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))))
% 6.68/6.90  (assume t3.a15 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))
% 6.68/6.90  (assume t3.a16 (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.a17 (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))
% 6.68/6.90  (assume t3.a18 (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.a19 (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))
% 6.68/6.90  (assume t3.a20 (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))))
% 6.68/6.90  (assume t3.a21 (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.a22 (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.a23 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.a24 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.a25 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.a26 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))
% 6.68/6.90  (assume t3.a27 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a28 (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))
% 6.68/6.90  (assume t3.a29 (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))))
% 6.68/6.90  (assume t3.a30 (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))
% 6.68/6.90  (assume t3.a31 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a32 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a33 (= tptp.c (tptp.inverse (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.a34 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.a35 (= tptp.b (tptp.inverse (tptp.inverse tptp.b))))
% 6.68/6.90  (assume t3.a36 (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.a37 (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a38 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a39 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a40 (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))))
% 6.68/6.90  (assume t3.a41 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a42 (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))))
% 6.68/6.90  (assume t3.a43 (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))
% 6.68/6.90  (assume t3.a44 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.a45 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))
% 6.68/6.90  (assume t3.a46 (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))
% 6.68/6.90  (assume t3.a47 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.a48 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))
% 6.68/6.90  (assume t3.a49 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))
% 6.68/6.90  (assume t3.a50 (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a51 (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a52 (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a53 (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a54 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))
% 6.68/6.90  (assume t3.a55 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))
% 6.68/6.90  (assume t3.a56 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a57 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))))
% 6.68/6.90  (assume t3.a58 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a59 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))))
% 6.68/6.90  (assume t3.a60 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))))
% 6.68/6.90  (assume t3.a61 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a62 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a63 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.a64 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a65 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 6.68/6.90  (assume t3.a66 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a67 (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))
% 6.68/6.90  (assume t3.a68 (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.a69 (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))
% 6.68/6.90  (assume t3.a70 (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))
% 6.68/6.90  (assume t3.a71 (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.a72 (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))))
% 6.68/6.90  (assume t3.a73 (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))))
% 6.68/6.90  (assume t3.a74 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 6.68/6.90  (assume t3.a75 (= tptp.b (tptp.multiply tptp.identity tptp.b)))
% 6.68/6.90  (assume t3.a76 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.a77 (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.a78 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))))
% 6.68/6.90  (assume t3.a79 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))))
% 6.68/6.90  (assume t3.a80 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))))
% 6.68/6.90  (assume t3.a81 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a82 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))
% 6.68/6.90  (assume t3.a83 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))))
% 6.68/6.90  (assume t3.a84 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))
% 6.68/6.90  (assume t3.a85 (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a86 (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 6.68/6.90  (assume t3.a87 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.a88 (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))))
% 6.68/6.90  (assume t3.a89 (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))))
% 6.68/6.90  (assume t3.a90 (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))))
% 6.68/6.90  (assume t3.a91 (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))))
% 6.68/6.90  (assume t3.a92 (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))
% 6.68/6.90  (assume t3.a93 (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))
% 6.68/6.90  (assume t3.a94 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))
% 6.68/6.90  (assume t3.a95 (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))
% 6.68/6.90  (step t3.t1 (cl (=> (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule implies_neg1)
% 6.68/6.90  (anchor :step t3.t2)
% 6.68/6.90  (assume t3.t2.a0 (= tptp.b (tptp.multiply tptp.identity tptp.b)))
% 6.68/6.90  (assume t3.t2.a1 (= tptp.identity (tptp.inverse tptp.identity)))
% 6.68/6.90  (assume t3.t2.a2 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.t2.a3 (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.t2.a4 (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))
% 6.68/6.90  (assume t3.t2.a5 (= tptp.c (tptp.inverse (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.t2.a6 (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.t2.a7 (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))
% 6.68/6.90  (assume t3.t2.a8 (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.t2.a9 (= tptp.b (tptp.inverse (tptp.inverse tptp.b))))
% 6.68/6.90  (assume t3.t2.a10 (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a11 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))))
% 6.68/6.90  (assume t3.t2.a12 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))
% 6.68/6.90  (assume t3.t2.a13 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a14 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a15 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))
% 6.68/6.90  (assume t3.t2.a16 (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))
% 6.68/6.90  (assume t3.t2.a17 (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)))
% 6.68/6.90  (assume t3.t2.a18 (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.t2.a19 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))
% 6.68/6.90  (assume t3.t2.a20 (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a21 (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))
% 6.68/6.90  (assume t3.t2.a22 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a23 (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a24 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a25 (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))
% 6.68/6.90  (assume t3.t2.a26 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))))
% 6.68/6.90  (assume t3.t2.a27 (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)))
% 6.68/6.90  (assume t3.t2.a28 (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.t2.a29 (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))
% 6.68/6.90  (assume t3.t2.a30 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a31 (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a32 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a33 (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))
% 6.68/6.90  (assume t3.t2.a34 (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))))
% 6.68/6.90  (assume t3.t2.a35 (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)))
% 6.68/6.90  (assume t3.t2.a36 (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))
% 6.68/6.90  (assume t3.t2.a37 (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))
% 6.68/6.90  (assume t3.t2.a38 (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.t2.a39 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))
% 6.68/6.90  (assume t3.t2.a40 (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a41 (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))))
% 6.68/6.90  (assume t3.t2.a42 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a43 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a44 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))))
% 6.68/6.90  (assume t3.t2.a45 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.t2.a46 (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.t2.a47 (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))))
% 6.68/6.90  (assume t3.t2.a48 (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))
% 6.68/6.90  (assume t3.t2.a49 (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))
% 6.68/6.90  (assume t3.t2.a50 (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.t2.a51 (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))
% 6.68/6.90  (assume t3.t2.a52 (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)))
% 6.68/6.90  (assume t3.t2.a53 (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a54 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))
% 6.68/6.90  (assume t3.t2.a55 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))
% 6.68/6.90  (assume t3.t2.a56 (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))))
% 6.68/6.90  (assume t3.t2.a57 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))))
% 6.68/6.90  (assume t3.t2.a58 (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))
% 6.68/6.90  (assume t3.t2.a59 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))))
% 6.68/6.90  (assume t3.t2.a60 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a61 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a62 (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))
% 6.68/6.90  (assume t3.t2.a63 (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))))
% 6.68/6.90  (assume t3.t2.a64 (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.t2.a65 (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))))
% 6.68/6.90  (assume t3.t2.a66 (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.t2.a67 (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))))
% 6.68/6.90  (assume t3.t2.a68 (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))))
% 6.68/6.90  (assume t3.t2.a69 (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.t2.a70 (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))))
% 6.68/6.90  (assume t3.t2.a71 (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))))
% 6.68/6.90  (assume t3.t2.a72 (= tptp.a (tptp.multiply tptp.identity tptp.a)))
% 6.68/6.90  (assume t3.t2.a73 (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))
% 6.68/6.90  (assume t3.t2.a74 (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.t2.a75 (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.t2.a76 (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))
% 6.68/6.90  (assume t3.t2.a77 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))
% 6.68/6.90  (assume t3.t2.a78 (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))
% 6.68/6.90  (assume t3.t2.a79 (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.t2.a80 (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.68/6.90  (assume t3.t2.a81 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))
% 6.68/6.90  (assume t3.t2.a82 (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))))
% 6.68/6.90  (assume t3.t2.a83 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))))
% 6.68/6.90  (assume t3.t2.a84 (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))
% 6.68/6.90  (assume t3.t2.a85 (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))
% 6.68/6.90  (assume t3.t2.a86 (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))))
% 6.68/6.90  (assume t3.t2.a87 (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))
% 6.68/6.90  (assume t3.t2.a88 (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))
% 6.68/6.90  (assume t3.t2.a89 (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))
% 6.68/6.90  (assume t3.t2.a90 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a91 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))))
% 6.68/6.90  (assume t3.t2.a92 (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a93 (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a94 (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.68/6.90  (assume t3.t2.a95 (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))
% 6.68/6.90  (step t3.t2.t1 (cl (= (tptp.least_upper_bound tptp.c tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) :rule symm :premises (t3.t2.a7))
% 6.68/6.90  (step t3.t2.t2 (cl (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule symm :premises (t3.t2.t1))
% 6.68/6.90  (step t3.t2.t3 (cl (= (tptp.inverse (tptp.inverse tptp.c)) tptp.c)) :rule symm :premises (t3.t2.a5))
% 6.68/6.90  (step t3.t2.t4 (cl (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.t3))
% 6.68/6.90  (step t3.t2.t5 (cl (= (tptp.inverse (tptp.inverse tptp.a)) tptp.a)) :rule symm :premises (t3.t2.a6))
% 6.68/6.90  (step t3.t2.t6 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule symm :premises (t3.t2.t5))
% 6.68/6.90  (step t3.t2.t7 (cl (= (tptp.least_upper_bound tptp.c tptp.a) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule cong :premises (t3.t2.t4 t3.t2.t6))
% 6.68/6.90  (step t3.t2.t8 (cl (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.a4))
% 6.68/6.90  (step t3.t2.t9 (cl (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.a3))
% 6.68/6.90  (step t3.t2.t10 (cl (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule trans :premises (t3.t2.t2 t3.t2.t7 t3.t2.t8 t3.t2.t9))
% 6.68/6.90  (step t3.t2.t11 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a8))
% 6.68/6.90  (step t3.t2.t12 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.t11))
% 6.68/6.90  (step t3.t2.t13 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t10 t3.t2.t12))
% 6.68/6.90  (step t3.t2.t14 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) tptp.identity)) :rule symm :premises (t3.t2.a2))
% 6.68/6.90  (step t3.t2.t15 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse tptp.identity))) :rule trans :premises (t3.t2.t13 t3.t2.t14 t3.t2.a1))
% 6.68/6.90  (step t3.t2.t16 (cl (= (tptp.inverse tptp.identity) tptp.identity)) :rule symm :premises (t3.t2.a1))
% 6.68/6.90  (step t3.t2.t17 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.identity)) :rule trans :premises (t3.t2.t15 t3.t2.t16))
% 6.68/6.90  (step t3.t2.t18 (cl (= tptp.a tptp.a)) :rule refl)
% 6.68/6.90  (step t3.t2.t19 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a) (tptp.multiply tptp.identity tptp.a))) :rule cong :premises (t3.t2.t17 t3.t2.t18))
% 6.68/6.90  (step t3.t2.t20 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) :rule symm :premises (t3.t2.t19))
% 6.68/6.90  (step t3.t2.t21 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule refl)
% 6.68/6.90  (step t3.t2.t22 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t16 t3.t2.t21))
% 6.68/6.90  (step t3.t2.t23 (cl (= (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a10))
% 6.68/6.90  (step t3.t2.t24 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule trans :premises (t3.t2.t22 t3.t2.t23 t3.t2.t12))
% 6.68/6.90  (step t3.t2.t25 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t10 t3.t2.t24))
% 6.68/6.90  (step t3.t2.t26 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse tptp.identity))) :rule trans :premises (t3.t2.t25 t3.t2.t14 t3.t2.a1))
% 6.68/6.90  (step t3.t2.t27 (cl (= (tptp.inverse tptp.identity) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t26))
% 6.68/6.90  (step t3.t2.t28 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t15 t3.t2.t27))
% 6.68/6.90  (step t3.t2.t29 (cl (= tptp.a (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) :rule trans :premises (t3.t2.a72 t3.t2.t20))
% 6.68/6.90  (step t3.t2.t30 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule cong :premises (t3.t2.t28 t3.t2.t29))
% 6.68/6.90  (step t3.t2.t31 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule symm :premises (t3.t2.a95))
% 6.68/6.90  (step t3.t2.t32 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule symm :premises (t3.t2.t31))
% 6.68/6.90  (step t3.t2.t33 (cl (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) :rule refl)
% 6.68/6.90  (step t3.t2.t34 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a34))
% 6.68/6.90  (step t3.t2.t35 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule symm :premises (t3.t2.t34))
% 6.68/6.90  (step t3.t2.t36 (cl (= (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.a))) :rule refl)
% 6.68/6.90  (step t3.t2.t37 (cl (= (tptp.multiply (tptp.inverse tptp.c) tptp.c) tptp.identity)) :rule symm :premises (t3.t2.a35))
% 6.68/6.90  (step t3.t2.t38 (cl (= (tptp.multiply (tptp.inverse tptp.c) tptp.c) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule trans :premises (t3.t2.t37 t3.t2.a36))
% 6.68/6.90  (step t3.t2.t39 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule cong :premises (t3.t2.t36 t3.t2.t38))
% 6.68/6.90  (step t3.t2.t40 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t3.t2.a37))
% 6.68/6.90  (step t3.t2.t41 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.a38))
% 6.68/6.90  (step t3.t2.t42 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t41 t3.t2.t11))
% 6.68/6.90  (step t3.t2.t43 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.a))) :rule cong :premises (t3.t2.t42 t3.t2.t18))
% 6.68/6.90  (step t3.t2.t44 (cl (= (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t22))
% 6.68/6.90  (step t3.t2.t45 (cl (= (tptp.multiply (tptp.inverse tptp.identity) tptp.identity) tptp.identity)) :rule symm :premises (t3.t2.a16))
% 6.68/6.90  (step t3.t2.t46 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule symm :premises (t3.t2.t45))
% 6.68/6.90  (step t3.t2.t47 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity)) :rule symm :premises (t3.t2.a15))
% 6.68/6.90  (step t3.t2.t48 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse tptp.identity))) :rule trans :premises (t3.t2.t47 t3.t2.a1))
% 6.68/6.90  (step t3.t2.t49 (cl (= (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.t48))
% 6.68/6.90  (step t3.t2.t50 (cl (= tptp.identity tptp.identity)) :rule refl)
% 6.68/6.90  (step t3.t2.t51 (cl (= (tptp.multiply (tptp.inverse tptp.identity) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity))) :rule cong :premises (t3.t2.t49 t3.t2.t50))
% 6.68/6.90  (step t3.t2.t52 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.t47))
% 6.68/6.91  (step t3.t2.t53 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t48 t3.t2.t52))
% 6.68/6.91  (step t3.t2.t54 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a14))
% 6.68/6.91  (step t3.t2.t55 (cl (= (tptp.inverse tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t16 t3.t2.t46 t3.t2.t51 t3.t2.t53 t3.t2.t54))
% 6.68/6.91  (step t3.t2.t56 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t55 t3.t2.t21))
% 6.68/6.91  (step t3.t2.t57 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a13))
% 6.68/6.91  (step t3.t2.t58 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t57))
% 6.68/6.91  (step t3.t2.t59 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.a10 t3.t2.t44 t3.t2.t56 t3.t2.t58))
% 6.68/6.91  (step t3.t2.t60 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.a) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a))) :rule cong :premises (t3.t2.t59 t3.t2.t18))
% 6.68/6.91  (step t3.t2.t61 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a))) :rule symm :premises (t3.t2.a89))
% 6.68/6.91  (step t3.t2.t62 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule symm :premises (t3.t2.t61))
% 6.68/6.91  (step t3.t2.t63 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule trans :premises (t3.t2.t35 t3.t2.t39 t3.t2.t40 t3.t2.t43 t3.t2.t60 t3.t2.t62))
% 6.68/6.91  (step t3.t2.t64 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.t63))
% 6.68/6.91  (step t3.t2.t65 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t33 t3.t2.t64))
% 6.68/6.91  (step t3.t2.t66 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a53))
% 6.68/6.91  (step t3.t2.t67 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t66))
% 6.68/6.91  (step t3.t2.t68 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule refl)
% 6.68/6.91  (step t3.t2.t69 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.a1 t3.t2.t68))
% 6.68/6.91  (step t3.t2.t70 (cl (= (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.a23))
% 6.68/6.91  (step t3.t2.t71 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a22))
% 6.68/6.91  (step t3.t2.t72 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.a21))
% 6.68/6.91  (step t3.t2.t73 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)))) :rule symm :premises (t3.t2.a18))
% 6.68/6.91  (step t3.t2.t74 (cl (= (tptp.least_upper_bound tptp.b tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) :rule symm :premises (t3.t2.a17))
% 6.68/6.91  (step t3.t2.t75 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t74))
% 6.68/6.91  (step t3.t2.t76 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t72 t3.t2.t73 t3.t2.t75))
% 6.68/6.91  (step t3.t2.t77 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t76 t3.t2.t33))
% 6.68/6.91  (step t3.t2.t78 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) tptp.identity)) :rule trans :premises (t3.t2.t71 t3.t2.t77 t3.t2.t47))
% 6.68/6.91  (step t3.t2.t79 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse tptp.identity))) :rule cong :premises (t3.t2.t78))
% 6.68/6.91  (step t3.t2.t80 (cl (= (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse tptp.identity))) :rule trans :premises (t3.t2.t70 t3.t2.t79))
% 6.68/6.91  (step t3.t2.t81 (cl (= (tptp.inverse tptp.identity) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t80))
% 6.68/6.91  (step t3.t2.t82 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t81 t3.t2.t68))
% 6.68/6.91  (step t3.t2.t83 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a94))
% 6.68/6.91  (step t3.t2.t84 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t83))
% 6.68/6.91  (step t3.t2.t85 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.a93))
% 6.68/6.91  (step t3.t2.t86 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t85))
% 6.68/6.91  (step t3.t2.t87 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule refl)
% 6.68/6.91  (step t3.t2.t88 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c))) :rule symm :premises (t3.t2.a91))
% 6.68/6.91  (step t3.t2.t89 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a90))
% 6.68/6.91  (step t3.t2.t90 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a30))
% 6.68/6.91  (step t3.t2.t91 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.a29))
% 6.68/6.91  (step t3.t2.t92 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule symm :premises (t3.t2.a28))
% 6.68/6.91  (step t3.t2.t93 (cl (= (tptp.greatest_lower_bound tptp.b tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) :rule symm :premises (t3.t2.a27))
% 6.68/6.91  (step t3.t2.t94 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t93))
% 6.68/6.91  (step t3.t2.t95 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t91 t3.t2.t92 t3.t2.t94))
% 6.68/6.91  (step t3.t2.t96 (cl (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) :rule refl)
% 6.68/6.91  (step t3.t2.t97 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t95 t3.t2.t96))
% 6.68/6.91  (step t3.t2.t98 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)) tptp.identity)) :rule symm :premises (t3.t2.a26))
% 6.68/6.91  (step t3.t2.t99 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse tptp.identity))) :rule trans :premises (t3.t2.t90 t3.t2.t97 t3.t2.t98 t3.t2.a1))
% 6.68/6.91  (step t3.t2.t100 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t99 t3.t2.t21))
% 6.68/6.91  (step t3.t2.t101 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t89 t3.t2.t100 t3.t2.t22 t3.t2.t23))
% 6.68/6.91  (step t3.t2.t102 (cl (= tptp.c tptp.c)) :rule refl)
% 6.68/6.91  (step t3.t2.t103 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.c))) :rule cong :premises (t3.t2.t101 t3.t2.t102))
% 6.68/6.91  (step t3.t2.t104 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.c))) :rule cong :premises (t3.t2.t21 t3.t2.t3))
% 6.68/6.91  (step t3.t2.t105 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.c) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.t104))
% 6.68/6.91  (step t3.t2.t106 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a87))
% 6.68/6.91  (step t3.t2.t107 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t88 t3.t2.t103 t3.t2.t105 t3.t2.t106))
% 6.68/6.91  (step t3.t2.t108 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t107 t3.t2.t68))
% 6.68/6.91  (step t3.t2.t109 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t108))
% 6.68/6.91  (step t3.t2.t110 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t109 t3.t2.a92))
% 6.68/6.91  (step t3.t2.t111 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule cong :premises (t3.t2.t87 t3.t2.t110))
% 6.68/6.91  (step t3.t2.t112 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule refl)
% 6.68/6.91  (step t3.t2.t113 (cl (= (tptp.inverse tptp.identity) (tptp.inverse tptp.identity))) :rule refl)
% 6.68/6.91  (step t3.t2.t114 (cl (= (tptp.inverse tptp.c) (tptp.inverse tptp.c))) :rule refl)
% 6.68/6.91  (step t3.t2.t115 (cl (= (tptp.greatest_lower_bound tptp.c tptp.a) (tptp.greatest_lower_bound tptp.a tptp.c))) :rule symm :premises (t3.t2.a52))
% 6.68/6.91  (step t3.t2.t116 (cl (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule symm :premises (t3.t2.t115))
% 6.68/6.91  (step t3.t2.t117 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule cong :premises (t3.t2.t114 t3.t2.t116))
% 6.68/6.91  (step t3.t2.t118 (cl (= (tptp.greatest_lower_bound tptp.c tptp.a) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule cong :premises (t3.t2.t4 t3.t2.t6))
% 6.68/6.91  (step t3.t2.t119 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.a51))
% 6.68/6.91  (step t3.t2.t120 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.a50))
% 6.68/6.91  (step t3.t2.t121 (cl (= (tptp.greatest_lower_bound tptp.c tptp.a) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule trans :premises (t3.t2.t118 t3.t2.t119 t3.t2.t120))
% 6.68/6.91  (step t3.t2.t122 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule cong :premises (t3.t2.t114 t3.t2.t121))
% 6.68/6.91  (step t3.t2.t123 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) :rule symm :premises (t3.t2.a49))
% 6.68/6.91  (step t3.t2.t124 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) :rule trans :premises (t3.t2.t117 t3.t2.t122 t3.t2.t123))
% 6.68/6.91  (step t3.t2.t125 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule cong :premises (t3.t2.t113 t3.t2.t124))
% 6.68/6.91  (step t3.t2.t126 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) :rule symm :premises (t3.t2.a48))
% 6.68/6.91  (step t3.t2.t127 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) :rule trans :premises (t3.t2.t67 t3.t2.t69 t3.t2.t125 t3.t2.t126))
% 6.68/6.91  (step t3.t2.t128 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule cong :premises (t3.t2.t112 t3.t2.t127))
% 6.68/6.91  (step t3.t2.t129 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.a47))
% 6.68/6.91  (step t3.t2.t130 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a46))
% 6.68/6.91  (step t3.t2.t131 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) tptp.c))) :rule cong :premises (t3.t2.t130 t3.t2.t102))
% 6.68/6.91  (step t3.t2.t132 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule refl)
% 6.68/6.91  (step t3.t2.t133 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) tptp.c) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t132 t3.t2.t4))
% 6.68/6.91  (step t3.t2.t134 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a45))
% 6.68/6.91  (step t3.t2.t135 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t131 t3.t2.t133 t3.t2.t134))
% 6.68/6.91  (step t3.t2.t136 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) tptp.identity))) :rule cong :premises (t3.t2.t135 t3.t2.t50))
% 6.68/6.91  (step t3.t2.t137 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.a) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.a))) :rule cong :premises (t3.t2.t11 t3.t2.t18))
% 6.68/6.91  (step t3.t2.t138 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a))) :rule symm :premises (t3.t2.t43))
% 6.68/6.91  (step t3.t2.t139 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule symm :premises (t3.t2.t39))
% 6.68/6.91  (step t3.t2.t140 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.a) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t137 t3.t2.t138 t3.t2.a37 t3.t2.t139 t3.t2.t34))
% 6.68/6.91  (step t3.t2.t141 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.a)) (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t140))
% 6.68/6.91  (step t3.t2.t142 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.a)))) :rule symm :premises (t3.t2.t141))
% 6.68/6.91  (step t3.t2.t143 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a39))
% 6.68/6.91  (step t3.t2.t144 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule symm :premises (t3.t2.t143))
% 6.68/6.91  (step t3.t2.t145 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.a))) :rule cong :premises (t3.t2.t21 t3.t2.t5))
% 6.68/6.91  (step t3.t2.t146 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.a) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.a))) :rule symm :premises (t3.t2.t137))
% 6.68/6.91  (step t3.t2.t147 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.a))) :rule trans :premises (t3.t2.t144 t3.t2.t145 t3.t2.t146))
% 6.68/6.91  (step t3.t2.t148 (cl (= (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.a)))) :rule cong :premises (t3.t2.t147))
% 6.68/6.91  (step t3.t2.t149 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.a)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t148))
% 6.68/6.91  (step t3.t2.t150 (cl (= (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a40))
% 6.68/6.91  (step t3.t2.t151 (cl (= (tptp.inverse tptp.a) (tptp.inverse tptp.a))) :rule refl)
% 6.68/6.91  (step t3.t2.t152 (cl (= tptp.identity (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t46 t3.t2.t51 t3.t2.t53 t3.t2.t54))
% 6.68/6.91  (step t3.t2.t153 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t33 t3.t2.t152))
% 6.68/6.91  (step t3.t2.t154 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) :rule symm :premises (t3.t2.t153))
% 6.68/6.91  (step t3.t2.t155 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))) :rule symm :premises (t3.t2.t10))
% 6.68/6.91  (step t3.t2.t156 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) :rule cong :premises (t3.t2.t155 t3.t2.t16))
% 6.68/6.91  (step t3.t2.t157 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule symm :premises (t3.t2.t156))
% 6.68/6.91  (step t3.t2.t158 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)) (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule symm :premises (t3.t2.a41))
% 6.68/6.91  (step t3.t2.t159 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t16 t3.t2.t12))
% 6.68/6.91  (step t3.t2.t160 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule trans :premises (t3.t2.t11 t3.t2.a10 t3.t2.t44 t3.t2.t159))
% 6.68/6.91  (step t3.t2.t161 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule cong :premises (t3.t2.t160))
% 6.68/6.91  (step t3.t2.t162 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.t161))
% 6.68/6.91  (step t3.t2.t163 (cl (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))) (tptp.least_upper_bound tptp.c tptp.a))) :rule symm :premises (t3.t2.t7))
% 6.68/6.91  (step t3.t2.t164 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) :rule trans :premises (t3.t2.a42 t3.t2.t154 t3.t2.t157 t3.t2.t158 t3.t2.t162 t3.t2.a3 t3.t2.a4 t3.t2.t163 t3.t2.t1))
% 6.68/6.91  (step t3.t2.t165 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t151 t3.t2.t164))
% 6.68/6.91  (step t3.t2.t166 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t165))
% 6.68/6.91  (step t3.t2.t167 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a43))
% 6.68/6.91  (step t3.t2.t168 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t142 t3.t2.t149 t3.t2.t150 t3.t2.t166 t3.t2.t167))
% 6.68/6.91  (step t3.t2.t169 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity))) :rule cong :premises (t3.t2.t168 t3.t2.t50))
% 6.68/6.91  (step t3.t2.t170 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity))) :rule symm :premises (t3.t2.a44))
% 6.68/6.91  (step t3.t2.t171 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule symm :premises (t3.t2.t170))
% 6.68/6.91  (step t3.t2.t172 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule refl)
% 6.68/6.91  (step t3.t2.t173 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity) (tptp.least_upper_bound tptp.a tptp.c))) :rule trans :premises (t3.t2.t157 t3.t2.t158 t3.t2.t162 t3.t2.a3 t3.t2.a4 t3.t2.t163 t3.t2.t1))
% 6.68/6.91  (step t3.t2.t174 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t172 t3.t2.t173))
% 6.68/6.91  (step t3.t2.t175 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t167))
% 6.68/6.91  (step t3.t2.t176 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t150))
% 6.68/6.91  (step t3.t2.t177 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t136 t3.t2.t169 t3.t2.t171 t3.t2.t174 t3.t2.t175 t3.t2.t165 t3.t2.t176 t3.t2.t148 t3.t2.t141))
% 6.68/6.91  (step t3.t2.t178 (cl (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) :rule refl)
% 6.68/6.91  (step t3.t2.t179 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t177 t3.t2.t178))
% 6.68/6.91  (step t3.t2.t180 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule cong :premises (t3.t2.t179))
% 6.68/6.91  (step t3.t2.t181 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t128 t3.t2.t129 t3.t2.t180))
% 6.68/6.91  (step t3.t2.t182 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a92))
% 6.68/6.91  (step t3.t2.t183 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))))) :rule refl)
% 6.68/6.91  (step t3.t2.t184 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule cong :premises (t3.t2.t183 t3.t2.t63))
% 6.68/6.91  (step t3.t2.t185 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule symm :premises (t3.t2.a88))
% 6.68/6.91  (step t3.t2.t186 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.t106))
% 6.68/6.91  (step t3.t2.t187 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) tptp.c) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))) :rule cong :premises (t3.t2.t12 t3.t2.t102))
% 6.68/6.91  (step t3.t2.t188 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))) :rule trans :premises (t3.t2.t186 t3.t2.t104 t3.t2.t187))
% 6.68/6.91  (step t3.t2.t189 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t188 t3.t2.t12))
% 6.68/6.91  (step t3.t2.t190 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t189))
% 6.68/6.91  (step t3.t2.t191 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t22 t3.t2.t23))
% 6.68/6.91  (step t3.t2.t192 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t183 t3.t2.t191))
% 6.68/6.91  (step t3.t2.t193 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t192))
% 6.68/6.91  (step t3.t2.t194 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t190 t3.t2.t193))
% 6.68/6.91  (step t3.t2.t195 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.t194))
% 6.68/6.91  (step t3.t2.t196 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a) tptp.a)) :rule symm :premises (t3.t2.t29))
% 6.68/6.91  (step t3.t2.t197 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) tptp.a))) :rule cong :premises (t3.t2.t195 t3.t2.t196))
% 6.68/6.91  (step t3.t2.t198 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule symm :premises (t3.t2.a85))
% 6.68/6.91  (step t3.t2.t199 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule symm :premises (t3.t2.t198))
% 6.68/6.91  (step t3.t2.t200 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) :rule symm :premises (t3.t2.a84))
% 6.68/6.91  (step t3.t2.t201 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule symm :premises (t3.t2.t200))
% 6.68/6.91  (step t3.t2.t202 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound tptp.c tptp.a))) :rule trans :premises (t3.t2.a3 t3.t2.a4 t3.t2.t163))
% 6.68/6.91  (step t3.t2.t203 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) :rule cong :premises (t3.t2.t114 t3.t2.t202))
% 6.68/6.91  (step t3.t2.t204 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) :rule cong :premises (t3.t2.t114 t3.t2.t2))
% 6.68/6.91  (step t3.t2.t205 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.t204))
% 6.68/6.91  (step t3.t2.t206 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t201 t3.t2.t203 t3.t2.t205))
% 6.68/6.91  (step t3.t2.t207 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t155 t3.t2.t206))
% 6.68/6.91  (step t3.t2.t208 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t199 t3.t2.t207))
% 6.68/6.91  (step t3.t2.t209 (cl (= (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule cong :premises (t3.t2.t208))
% 6.68/6.91  (step t3.t2.t210 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule symm :premises (t3.t2.t209))
% 6.68/6.91  (step t3.t2.t211 (cl (= (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.a86))
% 6.68/6.91  (step t3.t2.t212 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t210 t3.t2.t211 t3.t2.t190 t3.t2.t193))
% 6.68/6.91  (step t3.t2.t213 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t212))
% 6.68/6.91  (step t3.t2.t214 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t194 t3.t2.t213))
% 6.68/6.91  (step t3.t2.t215 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) tptp.a) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a))) :rule cong :premises (t3.t2.t214 t3.t2.t18))
% 6.68/6.91  (step t3.t2.t216 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule symm :premises (t3.t2.t211))
% 6.68/6.91  (step t3.t2.t217 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule cong :premises (t3.t2.t33 t3.t2.t204))
% 6.68/6.91  (step t3.t2.t218 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)))) :rule symm :premises (t3.t2.a83))
% 6.68/6.91  (step t3.t2.t219 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)))) :rule trans :premises (t3.t2.t217 t3.t2.t218))
% 6.68/6.91  (step t3.t2.t220 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))))) :rule cong :premises (t3.t2.t219))
% 6.68/6.91  (step t3.t2.t221 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))))) :rule symm :premises (t3.t2.a82))
% 6.68/6.91  (step t3.t2.t222 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule symm :premises (t3.t2.t221))
% 6.68/6.91  (step t3.t2.t223 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t1))
% 6.68/6.91  (step t3.t2.t224 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t191))
% 6.68/6.91  (step t3.t2.t225 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t223 t3.t2.t224))
% 6.68/6.91  (step t3.t2.t226 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.a79))
% 6.68/6.91  (step t3.t2.t227 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.t226))
% 6.68/6.91  (step t3.t2.t228 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t92 t3.t2.t94))
% 6.68/6.91  (step t3.t2.t229 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.t228))
% 6.68/6.91  (step t3.t2.t230 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule trans :premises (t3.t2.t130 t3.t2.t229))
% 6.68/6.91  (step t3.t2.t231 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule cong :premises (t3.t2.t230 t3.t2.t114))
% 6.68/6.91  (step t3.t2.t232 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule cong :premises (t3.t2.t92 t3.t2.t114))
% 6.68/6.91  (step t3.t2.t233 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)))) :rule symm :premises (t3.t2.a69))
% 6.68/6.91  (step t3.t2.t234 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.c) tptp.c) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c))) :rule cong :premises (t3.t2.a27 t3.t2.t102))
% 6.68/6.91  (step t3.t2.t235 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.c) tptp.c))) :rule symm :premises (t3.t2.t234))
% 6.68/6.91  (step t3.t2.t236 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.c) tptp.c)))) :rule cong :premises (t3.t2.t235))
% 6.68/6.91  (step t3.t2.t237 (cl (= (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c))) :rule symm :premises (t3.t2.a68))
% 6.68/6.91  (step t3.t2.t238 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule symm :premises (t3.t2.t237))
% 6.68/6.91  (step t3.t2.t239 (cl (= (tptp.greatest_lower_bound tptp.b tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule trans :premises (t3.t2.t93 t3.t2.t116))
% 6.68/6.91  (step t3.t2.t240 (cl (= (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule cong :premises (t3.t2.t102 t3.t2.t239))
% 6.68/6.91  (step t3.t2.t241 (cl (= (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)) tptp.c)) :rule symm :premises (t3.t2.a67))
% 6.68/6.91  (step t3.t2.t242 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.c) tptp.c) tptp.c)) :rule trans :premises (t3.t2.t234 t3.t2.t238 t3.t2.t240 t3.t2.t241))
% 6.68/6.91  (step t3.t2.t243 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.a tptp.c) tptp.c)) (tptp.inverse tptp.c))) :rule cong :premises (t3.t2.t242))
% 6.68/6.91  (step t3.t2.t244 (cl (= (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) :rule trans :premises (t3.t2.t231 t3.t2.t232 t3.t2.t233 t3.t2.t236 t3.t2.t243))
% 6.68/6.91  (step t3.t2.t245 (cl (= (tptp.inverse tptp.c) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.t244))
% 6.68/6.91  (step t3.t2.t246 (cl (= (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t6 t3.t2.t245))
% 6.68/6.91  (step t3.t2.t247 (cl (= (tptp.multiply tptp.c (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule cong :premises (t3.t2.t4 t3.t2.t114))
% 6.68/6.91  (step t3.t2.t248 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) tptp.identity)) :rule symm :premises (t3.t2.a78))
% 6.68/6.91  (step t3.t2.t249 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)) tptp.identity)) :rule symm :premises (t3.t2.a77))
% 6.68/6.91  (step t3.t2.t250 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule symm :premises (t3.t2.t249))
% 6.68/6.91  (step t3.t2.t251 (cl (= (tptp.multiply tptp.c (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule trans :premises (t3.t2.t247 t3.t2.t248 t3.t2.t250))
% 6.68/6.91  (step t3.t2.t252 (cl (= (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule cong :premises (t3.t2.t246 t3.t2.t251))
% 6.68/6.91  (step t3.t2.t253 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))))) :rule symm :premises (t3.t2.a76))
% 6.68/6.91  (step t3.t2.t254 (cl (= (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.a)))) :rule refl)
% 6.68/6.91  (step t3.t2.t255 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule cong :premises (t3.t2.t244 t3.t2.t151))
% 6.68/6.91  (step t3.t2.t256 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.a75))
% 6.68/6.91  (step t3.t2.t257 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule trans :premises (t3.t2.t255 t3.t2.t256))
% 6.68/6.91  (step t3.t2.t258 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t254 t3.t2.t257))
% 6.68/6.91  (step t3.t2.t259 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule refl)
% 6.68/6.91  (step t3.t2.t260 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t5 t3.t2.t259))
% 6.68/6.91  (step t3.t2.t261 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule trans :premises (t3.t2.t227 t3.t2.t252 t3.t2.t253 t3.t2.t258 t3.t2.t260))
% 6.68/6.91  (step t3.t2.t262 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule cong :premises (t3.t2.t261))
% 6.68/6.91  (step t3.t2.t263 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule cong :premises (t3.t2.t225 t3.t2.t262))
% 6.68/6.91  (step t3.t2.t264 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule trans :premises (t3.t2.t192 t3.t2.t189 t3.t2.t216 t3.t2.t209 t3.t2.t220 t3.t2.t222 t3.t2.t263))
% 6.68/6.91  (step t3.t2.t265 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule trans :premises (t3.t2.t212 t3.t2.t264))
% 6.68/6.91  (step t3.t2.t266 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule cong :premises (t3.t2.t265 t3.t2.t29))
% 6.68/6.91  (step t3.t2.t267 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule symm :premises (t3.t2.a81))
% 6.68/6.91  (step t3.t2.t268 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule symm :premises (t3.t2.t267))
% 6.68/6.91  (step t3.t2.t269 (cl (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule refl)
% 6.68/6.91  (step t3.t2.t270 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) tptp.a))) :rule cong :premises (t3.t2.t269 t3.t2.t196))
% 6.68/6.91  (step t3.t2.t271 (cl (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.t262))
% 6.68/6.91  (step t3.t2.t272 (cl (= (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) :rule refl)
% 6.68/6.91  (step t3.t2.t273 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t272 t3.t2.t11))
% 6.68/6.91  (step t3.t2.t274 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.t273))
% 6.68/6.91  (step t3.t2.t275 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule cong :premises (t3.t2.t272 t3.t2.t24))
% 6.68/6.91  (step t3.t2.t276 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.t275))
% 6.68/6.91  (step t3.t2.t277 (cl (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t271 t3.t2.a80 t3.t2.t274 t3.t2.t276))
% 6.68/6.91  (step t3.t2.t278 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.a80))
% 6.68/6.91  (step t3.t2.t279 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule symm :premises (t3.t2.a74))
% 6.68/6.91  (step t3.t2.t280 (cl (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule symm :premises (t3.t2.t279))
% 6.68/6.91  (step t3.t2.t281 (cl (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule trans :premises (t3.t2.t116 t3.t2.t118 t3.t2.t119 t3.t2.t120))
% 6.68/6.91  (step t3.t2.t282 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound tptp.a tptp.c))) :rule symm :premises (t3.t2.t281))
% 6.68/6.91  (step t3.t2.t283 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)))) :rule cong :premises (t3.t2.t282 t3.t2.t151))
% 6.68/6.91  (step t3.t2.t284 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)))) :rule trans :premises (t3.t2.t275 t3.t2.t273 t3.t2.t278 t3.t2.t262 t3.t2.t280 t3.t2.t283))
% 6.68/6.91  (step t3.t2.t285 (cl (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)))) :rule trans :premises (t3.t2.t277 t3.t2.t284))
% 6.68/6.91  (step t3.t2.t286 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule cong :premises (t3.t2.t285 t3.t2.t29))
% 6.68/6.91  (step t3.t2.t287 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule symm :premises (t3.t2.a73))
% 6.68/6.91  (step t3.t2.t288 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule symm :premises (t3.t2.t287))
% 6.68/6.91  (step t3.t2.t289 (cl (= (tptp.multiply tptp.identity tptp.a) tptp.a)) :rule symm :premises (t3.t2.a72))
% 6.68/6.91  (step t3.t2.t290 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t19 t3.t2.t289 t3.t2.a63))
% 6.68/6.91  (step t3.t2.t291 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t151 t3.t2.t290))
% 6.68/6.91  (step t3.t2.t292 (cl (= (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)) tptp.a)) :rule symm :premises (t3.t2.a63))
% 6.68/6.91  (step t3.t2.t293 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule cong :premises (t3.t2.t151 t3.t2.t292))
% 6.68/6.91  (step t3.t2.t294 (cl (= (tptp.multiply (tptp.inverse tptp.a) tptp.a) tptp.identity)) :rule symm :premises (t3.t2.a36))
% 6.68/6.91  (step t3.t2.t295 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) tptp.identity)) :rule trans :premises (t3.t2.t291 t3.t2.t293 t3.t2.t294))
% 6.68/6.91  (step t3.t2.t296 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity))) :rule cong :premises (t3.t2.t96 t3.t2.t295))
% 6.68/6.91  (step t3.t2.t297 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity))) :rule symm :premises (t3.t2.a71))
% 6.68/6.91  (step t3.t2.t298 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule symm :premises (t3.t2.t297))
% 6.68/6.91  (step t3.t2.t299 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule cong :premises (t3.t2.t6 t3.t2.a1))
% 6.68/6.91  (step t3.t2.t300 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)) (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule symm :premises (t3.t2.a65))
% 6.68/6.91  (step t3.t2.t301 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule trans :premises (t3.t2.t299 t3.t2.t300))
% 6.68/6.91  (step t3.t2.t302 (cl (= (tptp.multiply tptp.identity (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) :rule symm :premises (t3.t2.a64))
% 6.68/6.91  (step t3.t2.t303 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.inverse (tptp.inverse tptp.a)))) :rule cong :premises (t3.t2.t302))
% 6.68/6.91  (step t3.t2.t304 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) tptp.a)) :rule trans :premises (t3.t2.t303 t3.t2.t5))
% 6.68/6.91  (step t3.t2.t305 (cl (= (tptp.multiply tptp.a tptp.identity) (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t301 t3.t2.t304 t3.t2.a63))
% 6.68/6.91  (step t3.t2.t306 (cl (= (tptp.multiply tptp.c tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule cong :premises (t3.t2.t4 t3.t2.a1))
% 6.68/6.91  (step t3.t2.t307 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)) (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.a70))
% 6.68/6.91  (step t3.t2.t308 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse tptp.c)) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule cong :premises (t3.t2.t16 t3.t2.t114))
% 6.68/6.91  (step t3.t2.t309 (cl (= (tptp.multiply tptp.identity (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.t308))
% 6.68/6.91  (step t3.t2.t310 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse tptp.c)))) :rule cong :premises (t3.t2.t113 t3.t2.t244))
% 6.68/6.91  (step t3.t2.t311 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))) :rule symm :premises (t3.t2.t310))
% 6.68/6.91  (step t3.t2.t312 (cl (= (tptp.multiply tptp.identity (tptp.inverse tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))) :rule trans :premises (t3.t2.t309 t3.t2.t311))
% 6.68/6.91  (step t3.t2.t313 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))))) :rule cong :premises (t3.t2.t312))
% 6.68/6.91  (step t3.t2.t314 (cl (= (tptp.multiply tptp.identity (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) :rule symm :premises (t3.t2.a66))
% 6.68/6.91  (step t3.t2.t315 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.inverse tptp.c))) :rule trans :premises (t3.t2.t310 t3.t2.t308 t3.t2.t314))
% 6.68/6.91  (step t3.t2.t316 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.identity) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (tptp.inverse (tptp.inverse tptp.c)))) :rule cong :premises (t3.t2.t315))
% 6.68/6.91  (step t3.t2.t317 (cl (= (tptp.multiply tptp.c tptp.identity) tptp.c)) :rule trans :premises (t3.t2.t306 t3.t2.t307 t3.t2.t313 t3.t2.t316 t3.t2.t3))
% 6.68/6.91  (step t3.t2.t318 (cl (= (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)) (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)) tptp.c))) :rule cong :premises (t3.t2.t305 t3.t2.t317))
% 6.68/6.91  (step t3.t2.t319 (cl (= (tptp.greatest_lower_bound (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)) tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) :rule cong :premises (t3.t2.t292 t3.t2.t102))
% 6.68/6.91  (step t3.t2.t320 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.greatest_lower_bound tptp.a tptp.c))) :rule trans :premises (t3.t2.t270 t3.t2.t286 t3.t2.t288 t3.t2.t296 t3.t2.t298 t3.t2.t318 t3.t2.t319))
% 6.68/6.91  (step t3.t2.t321 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t24 t3.t2.t320))
% 6.68/6.91  (step t3.t2.t322 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule cong :premises (t3.t2.t11 t3.t2.t281))
% 6.68/6.91  (step t3.t2.t323 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a62))
% 6.68/6.91  (step t3.t2.t324 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule symm :premises (t3.t2.t158))
% 6.68/6.91  (step t3.t2.t325 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a42))
% 6.68/6.91  (step t3.t2.t326 (cl (= (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule trans :premises (t3.t2.t16 t3.t2.a55))
% 6.68/6.91  (step t3.t2.t327 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule trans :premises (t3.t2.t26 t3.t2.t326))
% 6.68/6.91  (step t3.t2.t328 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule cong :premises (t3.t2.t327 t3.t2.t33))
% 6.68/6.91  (step t3.t2.t329 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a61))
% 6.68/6.91  (step t3.t2.t330 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t329))
% 6.68/6.91  (step t3.t2.t331 (cl (= (tptp.inverse (tptp.inverse tptp.b)) tptp.b)) :rule symm :premises (t3.t2.a9))
% 6.68/6.91  (step t3.t2.t332 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t331 t3.t2.t178))
% 6.68/6.91  (step t3.t2.t333 (cl (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t2 t3.t2.t7 t3.t2.t8 t3.t2.t9 t3.t2.t161 t3.t2.t324 t3.t2.t156 t3.t2.t153 t3.t2.t325 t3.t2.t328 t3.t2.t330 t3.t2.t332))
% 6.68/6.91  (step t3.t2.t334 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule cong :premises (t3.t2.t230 t3.t2.t333))
% 6.68/6.91  (step t3.t2.t335 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a60))
% 6.68/6.91  (step t3.t2.t336 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule cong :premises (t3.t2.t228 t3.t2.a9))
% 6.68/6.91  (step t3.t2.t337 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b))) :rule symm :premises (t3.t2.t336))
% 6.68/6.91  (step t3.t2.t338 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b))) :rule trans :premises (t3.t2.a54 t3.t2.t337))
% 6.68/6.91  (step t3.t2.t339 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t338))
% 6.68/6.91  (step t3.t2.t340 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t339 t3.t2.t178))
% 6.68/6.91  (step t3.t2.t341 (cl (= tptp.b tptp.b)) :rule refl)
% 6.68/6.91  (step t3.t2.t342 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b))) :rule cong :premises (t3.t2.t230 t3.t2.t341))
% 6.68/6.91  (step t3.t2.t343 (cl (= (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a54))
% 6.68/6.91  (step t3.t2.t344 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t342 t3.t2.t336 t3.t2.t343))
% 6.68/6.91  (step t3.t2.t345 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) tptp.identity))) :rule cong :premises (t3.t2.t344 t3.t2.t50))
% 6.68/6.91  (step t3.t2.t346 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) tptp.identity) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity))) :rule cong :premises (t3.t2.t338 t3.t2.t50))
% 6.68/6.91  (step t3.t2.t347 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity))) :rule symm :premises (t3.t2.a59))
% 6.68/6.91  (step t3.t2.t348 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule symm :premises (t3.t2.t347))
% 6.68/6.91  (step t3.t2.t349 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule refl)
% 6.68/6.91  (step t3.t2.t350 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b) (tptp.multiply tptp.identity tptp.b))) :rule cong :premises (t3.t2.t17 t3.t2.t341))
% 6.68/6.91  (step t3.t2.t351 (cl (= (tptp.multiply tptp.identity tptp.b) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) :rule symm :premises (t3.t2.t350))
% 6.68/6.91  (step t3.t2.t352 (cl (= (tptp.inverse tptp.identity) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t15))
% 6.68/6.91  (step t3.t2.t353 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) :rule cong :premises (t3.t2.t352 t3.t2.t331))
% 6.68/6.91  (step t3.t2.t354 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))))) :rule symm :premises (t3.t2.t353))
% 6.68/6.91  (step t3.t2.t355 (cl (= (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))))) :rule trans :premises (t3.t2.t331 t3.t2.a0 t3.t2.t351 t3.t2.t354))
% 6.68/6.91  (step t3.t2.t356 (cl (= tptp.b (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) :rule trans :premises (t3.t2.a9 t3.t2.t355 t3.t2.t353))
% 6.68/6.91  (step t3.t2.t357 (cl (= (tptp.multiply tptp.b tptp.identity) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b) tptp.identity))) :rule cong :premises (t3.t2.t356 t3.t2.t50))
% 6.68/6.91  (step t3.t2.t358 (cl (= (tptp.multiply (tptp.inverse tptp.b) tptp.b) tptp.identity)) :rule symm :premises (t3.t2.a58))
% 6.68/6.91  (step t3.t2.t359 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule symm :premises (t3.t2.t358))
% 6.68/6.91  (step t3.t2.t360 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule cong :premises (t3.t2.t354 t3.t2.t359))
% 6.68/6.91  (step t3.t2.t361 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b))) :rule symm :premises (t3.t2.a57))
% 6.68/6.91  (step t3.t2.t362 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)))) :rule symm :premises (t3.t2.a56))
% 6.68/6.91  (step t3.t2.t363 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule symm :premises (t3.t2.t362))
% 6.68/6.91  (step t3.t2.t364 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) tptp.identity)) :rule symm :premises (t3.t2.a55))
% 6.68/6.91  (step t3.t2.t365 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (tptp.multiply (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity))) :rule cong :premises (t3.t2.t49 t3.t2.t364))
% 6.68/6.91  (step t3.t2.t366 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule symm :premises (t3.t2.t51))
% 6.68/6.91  (step t3.t2.t367 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.inverse tptp.identity))) :rule trans :premises (t3.t2.t363 t3.t2.t365 t3.t2.t366 t3.t2.t45 t3.t2.a1))
% 6.68/6.91  (step t3.t2.t368 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t367 t3.t2.t352))
% 6.68/6.91  (step t3.t2.t369 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) :rule cong :premises (t3.t2.t368 t3.t2.t341))
% 6.68/6.91  (step t3.t2.t370 (cl (= (tptp.multiply tptp.identity tptp.b) tptp.b)) :rule symm :premises (t3.t2.a0))
% 6.68/6.91  (step t3.t2.t371 (cl (= (tptp.multiply tptp.b tptp.identity) tptp.b)) :rule trans :premises (t3.t2.t357 t3.t2.t360 t3.t2.t361 t3.t2.t369 t3.t2.t350 t3.t2.t370))
% 6.68/6.91  (step t3.t2.t372 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b))) :rule cong :premises (t3.t2.t349 t3.t2.t371))
% 6.68/6.91  (step t3.t2.t373 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t345 t3.t2.t346 t3.t2.t348 t3.t2.t372 t3.t2.t336 t3.t2.t343))
% 6.68/6.91  (step t3.t2.t374 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t373 t3.t2.t178))
% 6.68/6.91  (step t3.t2.t375 (cl (= (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.t374))
% 6.68/6.91  (step t3.t2.t376 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t334 t3.t2.t335 t3.t2.t340 t3.t2.t375))
% 6.68/6.91  (step t3.t2.t377 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule cong :premises (t3.t2.t376))
% 6.68/6.91  (step t3.t2.t378 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule cong :premises (t3.t2.t374))
% 6.68/6.91  (step t3.t2.t379 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t182 t3.t2.t108 t3.t2.t184 t3.t2.t185 t3.t2.t197 t3.t2.t215 t3.t2.t266 t3.t2.t268 t3.t2.t321 t3.t2.t322 t3.t2.t323 t3.t2.t377 t3.t2.t378))
% 6.68/6.91  (step t3.t2.t380 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule cong :premises (t3.t2.t181 t3.t2.t379))
% 6.68/6.91  (step t3.t2.t381 (cl (= (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule symm :premises (t3.t2.a33))
% 6.68/6.91  (step t3.t2.t382 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a32))
% 6.68/6.91  (step t3.t2.t383 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule symm :premises (t3.t2.a31))
% 6.68/6.91  (step t3.t2.t384 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) tptp.identity)) :rule trans :premises (t3.t2.t90 t3.t2.t97 t3.t2.t98))
% 6.68/6.91  (step t3.t2.t385 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.inverse tptp.identity))) :rule cong :premises (t3.t2.t384))
% 6.68/6.91  (step t3.t2.t386 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.inverse tptp.identity))) :rule trans :premises (t3.t2.t383 t3.t2.t385))
% 6.68/6.91  (step t3.t2.t387 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t386 t3.t2.t178))
% 6.68/6.91  (step t3.t2.t388 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t16 t3.t2.t178))
% 6.68/6.91  (step t3.t2.t389 (cl (= (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) :rule symm :premises (t3.t2.a20))
% 6.68/6.91  (step t3.t2.t390 (cl (= (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t382 t3.t2.t387 t3.t2.t388 t3.t2.t389))
% 6.68/6.91  (step t3.t2.t391 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t390))
% 6.68/6.91  (step t3.t2.t392 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a24))
% 6.68/6.91  (step t3.t2.t393 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t80 t3.t2.t178))
% 6.68/6.91  (step t3.t2.t394 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t392 t3.t2.t393 t3.t2.t388 t3.t2.t389))
% 6.68/6.91  (step t3.t2.t395 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule cong :premises (t3.t2.t394))
% 6.68/6.91  (step t3.t2.t396 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule symm :premises (t3.t2.t395))
% 6.68/6.91  (step t3.t2.t397 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule trans :premises (t3.t2.t67 t3.t2.t69 t3.t2.t82 t3.t2.t84 t3.t2.t86 t3.t2.t111 t3.t2.t380 t3.t2.t381 t3.t2.t391 t3.t2.t396 t3.t2.a25))
% 6.68/6.91  (step t3.t2.t398 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule cong :premises (t3.t2.t33 t3.t2.t397))
% 6.68/6.91  (step t3.t2.t399 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule symm :premises (t3.t2.a25))
% 6.68/6.91  (step t3.t2.t400 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule trans :premises (t3.t2.t399 t3.t2.t395))
% 6.68/6.91  (step t3.t2.t401 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule cong :premises (t3.t2.t33 t3.t2.t400))
% 6.68/6.91  (step t3.t2.t402 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule symm :premises (t3.t2.a19))
% 6.68/6.91  (step t3.t2.t403 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule symm :premises (t3.t2.t402))
% 6.68/6.91  (step t3.t2.t404 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) :rule trans :premises (t3.t2.t73 t3.t2.t75))
% 6.68/6.91  (step t3.t2.t405 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule symm :premises (t3.t2.t404))
% 6.68/6.91  (step t3.t2.t406 (cl (= (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b))) :rule cong :premises (t3.t2.t405 t3.t2.t331))
% 6.68/6.91  (step t3.t2.t407 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule trans :premises (t3.t2.t404 t3.t2.t59))
% 6.68/6.91  (step t3.t2.t408 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b))) :rule cong :premises (t3.t2.t407 t3.t2.t341))
% 6.68/6.91  (step t3.t2.t409 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b))) :rule symm :premises (t3.t2.a12))
% 6.68/6.91  (step t3.t2.t410 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule symm :premises (t3.t2.t409))
% 6.68/6.91  (step t3.t2.t411 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule trans :premises (t3.t2.t403 t3.t2.t406 t3.t2.t408 t3.t2.t410))
% 6.68/6.91  (step t3.t2.t412 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule cong :premises (t3.t2.t33 t3.t2.t411))
% 6.68/6.91  (step t3.t2.t413 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule symm :premises (t3.t2.a11))
% 6.68/6.91  (step t3.t2.t414 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b)))))) :rule cong :premises (t3.t2.t26 t3.t2.t354))
% 6.68/6.91  (step t3.t2.t415 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) tptp.b)) :rule trans :premises (t3.t2.t353 t3.t2.t350 t3.t2.t370))
% 6.68/6.91  (step t3.t2.t416 (cl (= (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) :rule cong :premises (t3.t2.t352 t3.t2.t415))
% 6.68/6.91  (step t3.t2.t417 (cl (= tptp.a tptp.b)) :rule trans :premises (t3.t2.a72 t3.t2.t20 t3.t2.t30 t3.t2.t32 t3.t2.t65 t3.t2.t398 t3.t2.t401 t3.t2.t412 t3.t2.t413 t3.t2.t414 t3.t2.t416 t3.t2.t350 t3.t2.t370))
% 6.68/6.91  (step t3.t2 (cl (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (not (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) :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 t3.t2.a16 t3.t2.a17 t3.t2.a18 t3.t2.a19 t3.t2.a20 t3.t2.a21 t3.t2.a22 t3.t2.a23 t3.t2.a24 t3.t2.a25 t3.t2.a26 t3.t2.a27 t3.t2.a28 t3.t2.a29 t3.t2.a30 t3.t2.a31 t3.t2.a32 t3.t2.a33 t3.t2.a34 t3.t2.a35 t3.t2.a36 t3.t2.a37 t3.t2.a38 t3.t2.a39 t3.t2.a40 t3.t2.a41 t3.t2.a42 t3.t2.a43 t3.t2.a44 t3.t2.a45 t3.t2.a46 t3.t2.a47 t3.t2.a48 t3.t2.a49 t3.t2.a50 t3.t2.a51 t3.t2.a52 t3.t2.a53 t3.t2.a54 t3.t2.a55 t3.t2.a56 t3.t2.a57 t3.t2.a58 t3.t2.a59 t3.t2.a60 t3.t2.a61 t3.t2.a62 t3.t2.a63 t3.t2.a64 t3.t2.a65 t3.t2.a66 t3.t2.a67 t3.t2.a68 t3.t2.a69 t3.t2.a70 t3.t2.a71 t3.t2.a72 t3.t2.a73 t3.t2.a74 t3.t2.a75 t3.t2.a76 t3.t2.a77 t3.t2.a78 t3.t2.a79 t3.t2.a80 t3.t2.a81 t3.t2.a82 t3.t2.a83 t3.t2.a84 t3.t2.a85 t3.t2.a86 t3.t2.a87 t3.t2.a88 t3.t2.a89 t3.t2.a90 t3.t2.a91 t3.t2.a92 t3.t2.a93 t3.t2.a94 t3.t2.a95))
% 6.68/6.91  (step t3.t3 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule and_pos)
% 6.68/6.91  (step t3.t4 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.inverse tptp.identity))) :rule and_pos)
% 6.68/6.91  (step t3.t5 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t6 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t7 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 6.68/6.91  (step t3.t8 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule and_pos)
% 6.68/6.91  (step t3.t9 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 6.68/6.91  (step t3.t10 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule and_pos)
% 6.68/6.91  (step t3.t11 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.68/6.91  (step t3.t12 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) :rule and_pos)
% 6.68/6.91  (step t3.t13 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t14 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule and_pos)
% 6.68/6.91  (step t3.t15 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule and_pos)
% 6.68/6.91  (step t3.t16 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.68/6.91  (step t3.t17 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t18 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule and_pos)
% 6.68/6.91  (step t3.t19 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule and_pos)
% 6.68/6.91  (step t3.t20 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c))) :rule and_pos)
% 6.68/6.91  (step t3.t21 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.68/6.91  (step t3.t22 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule and_pos)
% 6.68/6.91  (step t3.t23 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t24 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule and_pos)
% 6.68/6.91  (step t3.t25 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t26 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.68/6.91  (step t3.t27 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.68/6.91  (step t3.t28 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule and_pos)
% 6.68/6.91  (step t3.t29 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule and_pos)
% 6.68/6.91  (step t3.t30 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c))) :rule and_pos)
% 6.68/6.91  (step t3.t31 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.68/6.91  (step t3.t32 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule and_pos)
% 6.68/6.91  (step t3.t33 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t34 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.68/6.91  (step t3.t35 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.68/6.91  (step t3.t36 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule and_pos)
% 6.68/6.91  (step t3.t37 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule and_pos)
% 6.68/6.91  (step t3.t38 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) :rule and_pos)
% 6.68/6.91  (step t3.t39 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 6.68/6.91  (step t3.t40 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 6.68/6.91  (step t3.t41 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule and_pos)
% 6.68/6.91  (step t3.t42 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 6.68/6.91  (step t3.t43 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.68/6.91  (step t3.t44 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule and_pos)
% 6.68/6.91  (step t3.t45 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t46 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t47 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule and_pos)
% 6.68/6.91  (step t3.t48 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule and_pos)
% 6.68/6.91  (step t3.t49 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.68/6.91  (step t3.t50 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule and_pos)
% 6.68/6.92  (step t3.t51 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule and_pos)
% 6.68/6.92  (step t3.t52 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule and_pos)
% 6.68/6.92  (step t3.t53 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule and_pos)
% 6.68/6.92  (step t3.t54 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 6.68/6.92  (step t3.t55 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule and_pos)
% 6.68/6.92  (step t3.t56 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule and_pos)
% 6.68/6.92  (step t3.t57 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule and_pos)
% 6.68/6.92  (step t3.t58 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule and_pos)
% 6.76/6.92  (step t3.t59 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule and_pos)
% 6.76/6.92  (step t3.t60 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule and_pos)
% 6.76/6.92  (step t3.t61 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule and_pos)
% 6.76/6.92  (step t3.t62 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule and_pos)
% 6.76/6.92  (step t3.t63 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.92  (step t3.t64 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.92  (step t3.t65 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule and_pos)
% 6.76/6.92  (step t3.t66 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule and_pos)
% 6.76/6.92  (step t3.t67 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.92  (step t3.t68 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule and_pos)
% 6.76/6.92  (step t3.t69 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.92  (step t3.t70 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule and_pos)
% 6.76/6.92  (step t3.t71 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule and_pos)
% 6.76/6.92  (step t3.t72 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.92  (step t3.t73 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule and_pos)
% 6.76/6.92  (step t3.t74 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule and_pos)
% 6.76/6.92  (step t3.t75 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 6.76/6.92  (step t3.t76 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule and_pos)
% 6.76/6.92  (step t3.t77 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.92  (step t3.t78 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.92  (step t3.t79 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 6.76/6.92  (step t3.t80 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.92  (step t3.t81 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.92  (step t3.t82 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule and_pos)
% 6.76/6.92  (step t3.t83 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.92  (step t3.t84 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule and_pos)
% 6.76/6.92  (step t3.t85 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule and_pos)
% 6.76/6.92  (step t3.t86 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule and_pos)
% 6.76/6.92  (step t3.t87 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule and_pos)
% 6.76/6.92  (step t3.t88 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule and_pos)
% 6.76/6.92  (step t3.t89 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule and_pos)
% 6.76/6.92  (step t3.t90 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule and_pos)
% 6.76/6.92  (step t3.t91 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule and_pos)
% 6.76/6.92  (step t3.t92 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule and_pos)
% 6.76/6.92  (step t3.t93 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.92  (step t3.t94 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) :rule and_pos)
% 6.76/6.92  (step t3.t95 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.92  (step t3.t96 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.92  (step t3.t97 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.92  (step t3.t98 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule and_pos)
% 6.76/6.92  (step t3.t99 (cl (= tptp.a tptp.b) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))))) :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 t3.t19 t3.t20 t3.t21 t3.t22 t3.t23 t3.t24 t3.t25 t3.t26 t3.t27 t3.t28 t3.t29 t3.t30 t3.t31 t3.t32 t3.t33 t3.t34 t3.t35 t3.t36 t3.t37 t3.t38 t3.t39 t3.t40 t3.t41 t3.t42 t3.t43 t3.t44 t3.t45 t3.t46 t3.t47 t3.t48 t3.t49 t3.t50 t3.t51 t3.t52 t3.t53 t3.t54 t3.t55 t3.t56 t3.t57 t3.t58 t3.t59 t3.t60 t3.t61 t3.t62 t3.t63 t3.t64 t3.t65 t3.t66 t3.t67 t3.t68 t3.t69 t3.t70 t3.t71 t3.t72 t3.t73 t3.t74 t3.t75 t3.t76 t3.t77 t3.t78 t3.t79 t3.t80 t3.t81 t3.t82 t3.t83 t3.t84 t3.t85 t3.t86 t3.t87 t3.t88 t3.t89 t3.t90 t3.t91 t3.t92 t3.t93 t3.t94 t3.t95 t3.t96 t3.t97 t3.t98))
% 6.76/6.94  (step t3.t100 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a tptp.b)) :rule reordering :premises (t3.t99))
% 6.76/6.95  (step t3.t101 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a tptp.b)) :rule contraction :premises (t3.t100))
% 6.76/6.95  (step t3.t102 (cl (=> (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) (= tptp.a tptp.b)) :rule resolution :premises (t3.t1 t3.t101))
% 6.76/6.95  (step t3.t103 (cl (=> (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) (not (= tptp.a tptp.b))) :rule implies_neg2)
% 6.76/6.95  (step t3.t104 (cl (=> (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) (=> (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b))) :rule resolution :premises (t3.t102 t3.t103))
% 6.76/6.96  (step t3.t105 (cl (=> (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b))) :rule contraction :premises (t3.t104))
% 6.76/6.96  (step t3.t106 (cl (not (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a tptp.b)) :rule implies :premises (t3.t105))
% 6.76/6.96  (step t3.t107 (cl (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (not (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule and_neg)
% 6.76/6.96  (step t3.t108 (cl (and (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule resolution :premises (t3.t107 t3.a75 t3.a2 t3.a24 t3.a21 t3.a30 t3.a33 t3.a34 t3.a5 t3.a9 t3.a35 t3.a37 t3.a83 t3.a55 t3.a38 t3.a27 t3.a15 t3.a3 t3.a1 t3.a10 t3.a48 t3.a53 t3.a17 t3.a32 t3.a50 t3.a62 t3.a93 t3.a14 t3.a0 t3.a8 t3.a19 t3.a31 t3.a51 t3.a64 t3.a92 t3.a40 t3.a12 t3.a11 t3.a65 t3.a16 t3.a45 t3.a66 t3.a42 t3.a39 t3.a58 t3.a80 t3.a47 t3.a7 t3.a91 t3.a67 t3.a43 t3.a22 t3.a28 t3.a4 t3.a52 t3.a49 t3.a26 t3.a57 t3.a78 t3.a13 t3.a79 t3.a81 t3.a56 t3.a70 t3.a6 t3.a76 t3.a73 t3.a77 t3.a20 t3.a29 t3.a36 t3.a72 t3.a88 t3.a74 t3.a95 t3.a71 t3.a18 t3.a86 t3.a25 t3.a23 t3.a63 t3.a68 t3.a94 t3.a90 t3.a59 t3.a46 t3.a69 t3.a89 t3.a44 t3.a84 t3.a54 t3.a41 t3.a60 t3.a87 t3.a85 t3.a61 t3.a82))
% 6.76/6.96  (step t3.t109 (cl (= tptp.a tptp.b)) :rule resolution :premises (t3.t106 t3.t108))
% 6.76/6.96  (step t3 (cl (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (not (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) :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 t3.a16 t3.a17 t3.a18 t3.a19 t3.a20 t3.a21 t3.a22 t3.a23 t3.a24 t3.a25 t3.a26 t3.a27 t3.a28 t3.a29 t3.a30 t3.a31 t3.a32 t3.a33 t3.a34 t3.a35 t3.a36 t3.a37 t3.a38 t3.a39 t3.a40 t3.a41 t3.a42 t3.a43 t3.a44 t3.a45 t3.a46 t3.a47 t3.a48 t3.a49 t3.a50 t3.a51 t3.a52 t3.a53 t3.a54 t3.a55 t3.a56 t3.a57 t3.a58 t3.a59 t3.a60 t3.a61 t3.a62 t3.a63 t3.a64 t3.a65 t3.a66 t3.a67 t3.a68 t3.a69 t3.a70 t3.a71 t3.a72 t3.a73 t3.a74 t3.a75 t3.a76 t3.a77 t3.a78 t3.a79 t3.a80 t3.a81 t3.a82 t3.a83 t3.a84 t3.a85 t3.a86 t3.a87 t3.a88 t3.a89 t3.a90 t3.a91 t3.a92 t3.a93 t3.a94 t3.a95))
% 6.76/6.96  (step t4 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c))) :rule and_pos)
% 6.76/6.96  (step t5 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c))) :rule and_pos)
% 6.76/6.96  (step t6 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.inverse tptp.identity))) :rule and_pos)
% 6.76/6.96  (step t7 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule and_pos)
% 6.76/6.96  (step t8 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule and_pos)
% 6.76/6.96  (step t9 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule and_pos)
% 6.76/6.96  (step t10 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t11 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t12 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t13 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t14 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t15 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule and_pos)
% 6.76/6.96  (step t16 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) :rule and_pos)
% 6.76/6.96  (step t17 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule and_pos)
% 6.76/6.96  (step t18 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t19 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t20 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.96  (step t21 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule and_pos)
% 6.76/6.96  (step t22 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.96  (step t23 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule and_pos)
% 6.76/6.96  (step t24 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule and_pos)
% 6.76/6.96  (step t25 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t26 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t27 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t28 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t29 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.96  (step t30 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule and_pos)
% 6.76/6.96  (step t31 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t32 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 6.76/6.96  (step t33 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t34 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 6.76/6.96  (step t35 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t36 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t37 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t38 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.96  (step t39 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) :rule and_pos)
% 6.76/6.96  (step t40 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t41 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t42 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.96  (step t43 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t44 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule and_pos)
% 6.76/6.96  (step t45 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.96  (step t46 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule and_pos)
% 6.76/6.96  (step t47 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule and_pos)
% 6.76/6.96  (step t48 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t49 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule and_pos)
% 6.76/6.96  (step t50 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule and_pos)
% 6.76/6.96  (step t51 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t52 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule and_pos)
% 6.76/6.96  (step t53 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule and_pos)
% 6.76/6.96  (step t54 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.96  (step t55 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.96  (step t56 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.96  (step t57 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.97  (step t58 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule and_pos)
% 6.76/6.97  (step t59 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule and_pos)
% 6.76/6.97  (step t60 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.97  (step t61 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule and_pos)
% 6.76/6.97  (step t62 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.97  (step t63 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule and_pos)
% 6.76/6.97  (step t64 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) :rule and_pos)
% 6.76/6.97  (step t65 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t66 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t67 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule and_pos)
% 6.76/6.97  (step t68 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t69 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule and_pos)
% 6.76/6.97  (step t70 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t71 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule and_pos)
% 6.76/6.97  (step t72 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule and_pos)
% 6.76/6.97  (step t73 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule and_pos)
% 6.76/6.97  (step t74 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t75 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.97  (step t76 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule and_pos)
% 6.76/6.97  (step t77 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule and_pos)
% 6.76/6.97  (step t78 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule and_pos)
% 6.76/6.97  (step t79 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule and_pos)
% 6.76/6.97  (step t80 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule and_pos)
% 6.76/6.97  (step t81 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule and_pos)
% 6.76/6.97  (step t82 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule and_pos)
% 6.76/6.97  (step t83 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule and_pos)
% 6.76/6.97  (step t84 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule and_pos)
% 6.76/6.97  (step t85 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t86 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule and_pos)
% 6.76/6.97  (step t87 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule and_pos)
% 6.76/6.97  (step t88 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule and_pos)
% 6.76/6.97  (step t89 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t90 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule and_pos)
% 6.76/6.97  (step t91 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t92 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule and_pos)
% 6.76/6.97  (step t93 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule and_pos)
% 6.76/6.97  (step t94 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule and_pos)
% 6.76/6.97  (step t95 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule and_pos)
% 6.76/6.97  (step t96 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule and_pos)
% 6.76/6.97  (step t97 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule and_pos)
% 6.76/6.97  (step t98 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule and_pos)
% 6.76/6.97  (step t99 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule and_pos)
% 6.76/6.97  (step t100 (cl (= tptp.a tptp.b) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))))) :rule resolution :premises (t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23 t24 t25 t26 t27 t28 t29 t30 t31 t32 t33 t34 t35 t36 t37 t38 t39 t40 t41 t42 t43 t44 t45 t46 t47 t48 t49 t50 t51 t52 t53 t54 t55 t56 t57 t58 t59 t60 t61 t62 t63 t64 t65 t66 t67 t68 t69 t70 t71 t72 t73 t74 t75 t76 t77 t78 t79 t80 t81 t82 t83 t84 t85 t86 t87 t88 t89 t90 t91 t92 t93 t94 t95 t96 t97 t98 t99))
% 6.76/6.99  (step t101 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a tptp.b)) :rule reordering :premises (t100))
% 6.76/7.00  (step t102 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a tptp.b)) :rule contraction :premises (t101))
% 6.76/7.00  (step t103 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) (= tptp.a tptp.b)) :rule resolution :premises (t2 t102))
% 6.76/7.00  (step t104 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) (not (= tptp.a tptp.b))) :rule implies_neg2)
% 6.76/7.00  (step t105 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b))) :rule resolution :premises (t103 t104))
% 6.76/7.00  (step t106 (cl (=> (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b))) :rule contraction :premises (t105))
% 6.76/7.00  (step t107 (cl (not (and (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c)) (= tptp.identity (tptp.inverse tptp.identity)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))) (= tptp.a (tptp.multiply tptp.identity tptp.a)) (= tptp.b (tptp.multiply tptp.identity tptp.b)) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) (= tptp.a tptp.b)) :rule implies :premises (t106))
% 6.76/7.00  (step t108 (cl (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c))) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (not (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= tptp.a tptp.b)) :rule resolution :premises (t1 t107))
% 6.76/7.00  (step t109 (cl (= tptp.a tptp.b) (not (= tptp.identity (tptp.inverse tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.b tptp.c))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.b tptp.c))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (not (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule reordering :premises (t108))
% 6.76/7.01  (step t110 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t111)
% 6.76/7.01  (assume t111.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t111.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.c)) (:= Y (tptp.inverse tptp.a)) (:= Z (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))
% 6.76/7.01  (step t111.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule or :premises (t111.t1))
% 6.76/7.01  (step t111.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t111.t2 t111.a0))
% 6.76/7.01  (step t111 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule subproof :discharge (t111.a0))
% 6.76/7.01  (step t112 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t110 t111))
% 6.76/7.01  (step t113 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t114 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule resolution :premises (t112 t113))
% 6.76/7.01  (step t115 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule contraction :premises (t114))
% 6.76/7.01  (step t116 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule implies :premises (t115))
% 6.76/7.01  (step t117 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.inverse tptp.a)) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t116 a2))
% 6.76/7.01  (step t118 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t119)
% 6.76/7.01  (assume t119.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t119.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Y (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (:= Z (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))
% 6.76/7.01  (step t119.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule or :premises (t119.t1))
% 6.76/7.01  (step t119.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t119.t2 t119.a0))
% 6.76/7.01  (step t119 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule subproof :discharge (t119.a0))
% 6.76/7.01  (step t120 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t118 t119))
% 6.76/7.01  (step t121 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t122 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule resolution :premises (t120 t121))
% 6.76/7.01  (step t123 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule contraction :premises (t122))
% 6.76/7.01  (step t124 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule implies :premises (t123))
% 6.76/7.01  (step t125 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t124 a2))
% 6.76/7.01  (step t126 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t127)
% 6.76/7.01  (assume t127.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t127.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (:= Y (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.76/7.01  (step t127.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule or :premises (t127.t1))
% 6.76/7.01  (step t127.t3 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t127.t2 t127.a0))
% 6.76/7.01  (step t127 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule subproof :discharge (t127.a0))
% 6.76/7.01  (step t128 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t126 t127))
% 6.76/7.01  (step t129 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule implies_neg2)
% 6.76/7.01  (step t130 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule resolution :premises (t128 t129))
% 6.76/7.01  (step t131 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule contraction :premises (t130))
% 6.76/7.01  (step t132 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies :premises (t131))
% 6.76/7.01  (step t133 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t132 a21))
% 6.76/7.01  (step t134 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t135)
% 6.76/7.01  (assume t135.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t135.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (:= Y (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))
% 6.76/7.01  (step t135.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule or :premises (t135.t1))
% 6.76/7.01  (step t135.t3 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t135.t2 t135.a0))
% 6.76/7.01  (step t135 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule subproof :discharge (t135.a0))
% 6.76/7.01  (step t136 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t134 t135))
% 6.76/7.01  (step t137 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule implies_neg2)
% 6.76/7.01  (step t138 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule resolution :premises (t136 t137))
% 6.76/7.01  (step t139 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))))) :rule contraction :premises (t138))
% 6.76/7.01  (step t140 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies :premises (t139))
% 6.76/7.01  (step t141 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.inverse (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t140 a20))
% 6.76/7.01  (step t142 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t143)
% 6.76/7.01  (assume t143.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t143.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (:= Y (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t143.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule or :premises (t143.t1))
% 6.76/7.01  (step t143.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule resolution :premises (t143.t2 t143.a0))
% 6.76/7.01  (step t143 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule subproof :discharge (t143.a0))
% 6.76/7.01  (step t144 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule resolution :premises (t142 t143))
% 6.76/7.01  (step t145 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))))) :rule implies_neg2)
% 6.76/7.01  (step t146 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))))) :rule resolution :premises (t144 t145))
% 6.76/7.01  (step t147 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)))))) :rule contraction :premises (t146))
% 6.76/7.01  (step t148 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule implies :premises (t147))
% 6.76/7.01  (step t149 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity))))) :rule resolution :premises (t148 a17))
% 6.76/7.01  (step t150 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t151)
% 6.76/7.01  (assume t151.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t151.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (:= Y (tptp.least_upper_bound tptp.c tptp.a))))
% 6.76/7.01  (step t151.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule or :premises (t151.t1))
% 6.76/7.01  (step t151.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule resolution :premises (t151.t2 t151.a0))
% 6.76/7.01  (step t151 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule subproof :discharge (t151.a0))
% 6.76/7.01  (step t152 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule resolution :premises (t150 t151))
% 6.76/7.01  (step t153 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t154 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))))) :rule resolution :premises (t152 t153))
% 6.76/7.01  (step t155 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))))))) :rule contraction :premises (t154))
% 6.76/7.01  (step t156 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule implies :premises (t155))
% 6.76/7.01  (step t157 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.c tptp.a)) (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)))))) :rule resolution :premises (t156 a17))
% 6.76/7.01  (step t158 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t159)
% 6.76/7.01  (assume t159.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 6.76/7.01  (step t159.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))
% 6.76/7.01  (step t159.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule or :premises (t159.t1))
% 6.76/7.01  (step t159.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule resolution :premises (t159.t2 t159.a0))
% 6.76/7.01  (step t159 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule subproof :discharge (t159.a0))
% 6.76/7.01  (step t160 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule resolution :premises (t158 t159))
% 6.76/7.01  (step t161 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (not (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))))) :rule implies_neg2)
% 6.76/7.01  (step t162 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))))) :rule resolution :premises (t160 t161))
% 6.76/7.01  (step t163 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))))) :rule contraction :premises (t162))
% 6.76/7.01  (step t164 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule implies :premises (t163))
% 6.76/7.01  (step t165 (cl (not (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) (not (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule equiv_pos2)
% 6.76/7.01  (anchor :step t166 :args ((X $$unsorted) (:= X X)))
% 6.76/7.01  (step t166.t1 (cl (= X X)) :rule refl)
% 6.76/7.01  (step t166.t2 (cl (= (= (tptp.inverse (tptp.inverse X)) X) (= X (tptp.inverse (tptp.inverse X))))) :rule all_simplify)
% 6.76/7.01  (step t166 (cl (= (forall ((X $$unsorted)) (= (tptp.inverse (tptp.inverse X)) X)) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))) :rule bind)
% 6.76/7.01  (step t167 (cl (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule resolution :premises (t165 t166 a16))
% 6.76/7.01  (step t168 (cl (= (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule resolution :premises (t164 t167))
% 6.76/7.01  (step t169 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t170)
% 6.76/7.01  (assume t170.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t170.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z tptp.c) (:= X tptp.identity)))
% 6.76/7.01  (step t170.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule or :premises (t170.t1))
% 6.76/7.01  (step t170.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule resolution :premises (t170.t2 t170.a0))
% 6.76/7.01  (step t170 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule subproof :discharge (t170.a0))
% 6.76/7.01  (step t171 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule resolution :premises (t169 t170))
% 6.76/7.01  (step t172 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (not (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))))) :rule implies_neg2)
% 6.76/7.01  (step t173 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))))) :rule resolution :premises (t171 t172))
% 6.76/7.01  (step t174 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity))))) :rule contraction :premises (t173))
% 6.76/7.01  (step t175 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule implies :premises (t174))
% 6.76/7.01  (step t176 (cl (= (tptp.multiply (tptp.greatest_lower_bound tptp.a tptp.c) tptp.identity) (tptp.greatest_lower_bound (tptp.multiply tptp.a tptp.identity) (tptp.multiply tptp.c tptp.identity)))) :rule resolution :premises (t175 a14))
% 6.76/7.01  (step t177 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t178)
% 6.76/7.01  (assume t178.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t178.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= Y (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (:= Z (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (:= X (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t178.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule or :premises (t178.t1))
% 6.76/7.01  (step t178.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t178.t2 t178.a0))
% 6.76/7.01  (step t178 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule subproof :discharge (t178.a0))
% 6.76/7.01  (step t179 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t177 t178))
% 6.76/7.01  (step t180 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t181 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule resolution :premises (t179 t180))
% 6.76/7.01  (step t182 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule contraction :premises (t181))
% 6.76/7.01  (step t183 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule implies :premises (t182))
% 6.76/7.01  (step t184 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t183 a13))
% 6.76/7.01  (step t185 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t186)
% 6.76/7.01  (assume t186.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 6.76/7.01  (step t186.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (:= Z (tptp.inverse tptp.a))))
% 6.76/7.01  (step t186.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule or :premises (t186.t1))
% 6.76/7.01  (step t186.t3 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t186.t2 t186.a0))
% 6.76/7.01  (step t186 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule subproof :discharge (t186.a0))
% 6.76/7.01  (step t187 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t185 t186))
% 6.76/7.01  (step t188 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (not (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t189 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule resolution :premises (t187 t188))
% 6.76/7.01  (step t190 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))))) :rule contraction :premises (t189))
% 6.76/7.01  (step t191 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.least_upper_bound Y Z)) (tptp.least_upper_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies :premises (t190))
% 6.76/7.01  (step t192 (cl (= (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.least_upper_bound (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c)) (tptp.inverse tptp.a))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.greatest_lower_bound (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t191 a11))
% 6.76/7.01  (step t193 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t194)
% 6.76/7.01  (assume t194.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 6.76/7.01  (step t194.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (:= Y (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))
% 6.76/7.01  (step t194.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule or :premises (t194.t1))
% 6.76/7.01  (step t194.t3 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t194.t2 t194.a0))
% 6.76/7.01  (step t194 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule subproof :discharge (t194.a0))
% 6.76/7.01  (step t195 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t193 t194))
% 6.76/7.01  (step t196 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t197 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule resolution :premises (t195 t196))
% 6.76/7.01  (step t198 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule contraction :premises (t197))
% 6.76/7.01  (step t199 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule implies :premises (t198))
% 6.76/7.01  (step t200 (cl (= (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t199 a4))
% 6.76/7.01  (step t201 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t202)
% 6.76/7.01  (assume t202.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t202.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) (:= Y (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))
% 6.76/7.01  (step t202.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule or :premises (t202.t1))
% 6.76/7.01  (step t202.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t202.t2 t202.a0))
% 6.76/7.01  (step t202 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule subproof :discharge (t202.a0))
% 6.76/7.01  (step t203 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t201 t202))
% 6.76/7.01  (step t204 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t205 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule resolution :premises (t203 t204))
% 6.76/7.01  (step t206 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule contraction :premises (t205))
% 6.76/7.01  (step t207 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule implies :premises (t206))
% 6.76/7.01  (step t208 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t207 a2))
% 6.76/7.01  (step t209 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t210)
% 6.76/7.01  (assume t210.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t210.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.c)) (:= Y (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))
% 6.76/7.01  (step t210.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule or :premises (t210.t1))
% 6.76/7.01  (step t210.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule resolution :premises (t210.t2 t210.a0))
% 6.76/7.01  (step t210 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule subproof :discharge (t210.a0))
% 6.76/7.01  (step t211 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule resolution :premises (t209 t210))
% 6.76/7.01  (step t212 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))))) :rule implies_neg2)
% 6.76/7.01  (step t213 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))))) :rule resolution :premises (t211 t212))
% 6.76/7.01  (step t214 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))))) :rule contraction :premises (t213))
% 6.76/7.01  (step t215 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule implies :premises (t214))
% 6.76/7.01  (step t216 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule resolution :premises (t215 a2))
% 6.76/7.01  (step t217 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t218)
% 6.76/7.01  (assume t218.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t218.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.c)) (:= Y (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))
% 6.76/7.01  (step t218.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule or :premises (t218.t1))
% 6.76/7.01  (step t218.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t218.t2 t218.a0))
% 6.76/7.01  (step t218 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule subproof :discharge (t218.a0))
% 6.76/7.01  (step t219 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t217 t218))
% 6.76/7.01  (step t220 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t221 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule resolution :premises (t219 t220))
% 6.76/7.01  (step t222 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))))) :rule contraction :premises (t221))
% 6.76/7.01  (step t223 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule implies :premises (t222))
% 6.76/7.01  (step t224 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t223 a2))
% 6.76/7.01  (step t225 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t226)
% 6.76/7.01  (assume t226.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t226.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (:= Y tptp.b) (:= Z (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t226.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule or :premises (t226.t1))
% 6.76/7.01  (step t226.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t226.t2 t226.a0))
% 6.76/7.01  (step t226 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule subproof :discharge (t226.a0))
% 6.76/7.01  (step t227 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t225 t226))
% 6.76/7.01  (step t228 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t229 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t227 t228))
% 6.76/7.01  (step t230 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule contraction :premises (t229))
% 6.76/7.01  (step t231 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies :premises (t230))
% 6.76/7.01  (step t232 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t231 a2))
% 6.76/7.01  (step t233 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t234)
% 6.76/7.01  (assume t234.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t234.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (:= Y (tptp.least_upper_bound tptp.a tptp.c)) (:= Z tptp.identity)))
% 6.76/7.01  (step t234.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule or :premises (t234.t1))
% 6.76/7.01  (step t234.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule resolution :premises (t234.t2 t234.a0))
% 6.76/7.01  (step t234 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule subproof :discharge (t234.a0))
% 6.76/7.01  (step t235 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule resolution :premises (t233 t234))
% 6.76/7.01  (step t236 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))))) :rule implies_neg2)
% 6.76/7.01  (step t237 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))))) :rule resolution :premises (t235 t236))
% 6.76/7.01  (step t238 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity))))) :rule contraction :premises (t237))
% 6.76/7.01  (step t239 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule implies :premises (t238))
% 6.76/7.01  (step t240 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) tptp.identity) (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) tptp.identity)))) :rule resolution :premises (t239 a2))
% 6.76/7.01  (step t241 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t242)
% 6.76/7.01  (assume t242.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t242.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))) (:= Y tptp.b) (:= Z tptp.identity)))
% 6.76/7.01  (step t242.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule or :premises (t242.t1))
% 6.76/7.01  (step t242.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule resolution :premises (t242.t2 t242.a0))
% 6.76/7.01  (step t242 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule subproof :discharge (t242.a0))
% 6.76/7.01  (step t243 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule resolution :premises (t241 t242))
% 6.76/7.01  (step t244 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))))) :rule implies_neg2)
% 6.76/7.01  (step t245 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))))) :rule resolution :premises (t243 t244))
% 6.76/7.01  (step t246 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity))))) :rule contraction :premises (t245))
% 6.76/7.01  (step t247 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule implies :premises (t246))
% 6.76/7.01  (step t248 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) tptp.b) tptp.identity) (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.multiply tptp.b tptp.identity)))) :rule resolution :premises (t247 a2))
% 6.76/7.01  (step t249 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t250)
% 6.76/7.01  (assume t250.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t250.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b)))) (:= Y (tptp.inverse tptp.b)) (:= Z tptp.b)))
% 6.76/7.01  (step t250.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule or :premises (t250.t1))
% 6.76/7.01  (step t250.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule resolution :premises (t250.t2 t250.a0))
% 6.76/7.01  (step t250 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule subproof :discharge (t250.a0))
% 6.76/7.01  (step t251 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule resolution :premises (t249 t250))
% 6.76/7.01  (step t252 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))))) :rule implies_neg2)
% 6.76/7.01  (step t253 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))))) :rule resolution :premises (t251 t252))
% 6.76/7.01  (step t254 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b))))) :rule contraction :premises (t253))
% 6.76/7.01  (step t255 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule implies :premises (t254))
% 6.76/7.01  (step t256 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule resolution :premises (t255 a2))
% 6.76/7.01  (step t257 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t258)
% 6.76/7.01  (assume t258.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 6.76/7.01  (step t258.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.c))))
% 6.76/7.01  (step t258.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule or :premises (t258.t1))
% 6.76/7.01  (step t258.t3 (cl (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule resolution :premises (t258.t2 t258.a0))
% 6.76/7.01  (step t258 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule subproof :discharge (t258.a0))
% 6.76/7.01  (step t259 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule resolution :premises (t257 t258))
% 6.76/7.01  (step t260 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (not (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t261 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))))) :rule resolution :premises (t259 t260))
% 6.76/7.01  (step t262 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c))))) :rule contraction :premises (t261))
% 6.76/7.01  (step t263 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule implies :premises (t262))
% 6.76/7.01  (step t264 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) (not (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule equiv_pos2)
% 6.76/7.01  (anchor :step t265 :args ((X $$unsorted) (:= X X)))
% 6.76/7.01  (step t265.t1 (cl (= X X)) :rule refl)
% 6.76/7.01  (step t265.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 6.76/7.01  (step t265 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 6.76/7.01  (step t266 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t264 t265 a0))
% 6.76/7.01  (step t267 (cl (= (tptp.inverse tptp.c) (tptp.multiply tptp.identity (tptp.inverse tptp.c)))) :rule resolution :premises (t263 t266))
% 6.76/7.01  (step t268 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t269)
% 6.76/7.01  (assume t269.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 6.76/7.01  (step t269.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 6.76/7.01  (step t269.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule or :premises (t269.t1))
% 6.76/7.01  (step t269.t3 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t269.t2 t269.a0))
% 6.76/7.01  (step t269 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule subproof :discharge (t269.a0))
% 6.76/7.01  (step t270 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t268 t269))
% 6.76/7.01  (step t271 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (not (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t272 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule resolution :premises (t270 t271))
% 6.76/7.01  (step t273 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a))))) :rule contraction :premises (t272))
% 6.76/7.01  (step t274 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule implies :premises (t273))
% 6.76/7.01  (step t275 (cl (= (tptp.inverse tptp.a) (tptp.multiply tptp.identity (tptp.inverse tptp.a)))) :rule resolution :premises (t274 t266))
% 6.76/7.01  (step t276 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t277)
% 6.76/7.01  (assume t277.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 6.76/7.01  (step t277.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule forall_inst :args ((:= X tptp.b)))
% 6.76/7.01  (step t277.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule or :premises (t277.t1))
% 6.76/7.01  (step t277.t3 (cl (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule resolution :premises (t277.t2 t277.a0))
% 6.76/7.01  (step t277 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule subproof :discharge (t277.a0))
% 6.76/7.01  (step t278 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule resolution :premises (t276 t277))
% 6.76/7.01  (step t279 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (not (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule implies_neg2)
% 6.76/7.01  (step t280 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule resolution :premises (t278 t279))
% 6.76/7.01  (step t281 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.b (tptp.multiply tptp.identity tptp.b)))) :rule contraction :premises (t280))
% 6.76/7.01  (step t282 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule implies :premises (t281))
% 6.76/7.01  (step t283 (cl (= tptp.b (tptp.multiply tptp.identity tptp.b))) :rule resolution :premises (t282 t266))
% 6.76/7.01  (step t284 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t285)
% 6.76/7.01  (assume t285.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 6.76/7.01  (step t285.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 6.76/7.01  (step t285.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule or :premises (t285.t1))
% 6.76/7.01  (step t285.t3 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t285.t2 t285.a0))
% 6.76/7.01  (step t285 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule subproof :discharge (t285.a0))
% 6.76/7.01  (step t286 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t284 t285))
% 6.76/7.01  (step t287 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule implies_neg2)
% 6.76/7.01  (step t288 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t286 t287))
% 6.76/7.01  (step t289 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= tptp.a (tptp.multiply tptp.identity tptp.a)))) :rule contraction :premises (t288))
% 6.76/7.01  (step t290 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule implies :premises (t289))
% 6.76/7.01  (step t291 (cl (= tptp.a (tptp.multiply tptp.identity tptp.a))) :rule resolution :premises (t290 t266))
% 6.76/7.01  (step t292 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t293)
% 6.76/7.01  (assume t293.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t293.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.inverse tptp.a))))
% 6.76/7.01  (step t293.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule or :premises (t293.t1))
% 6.76/7.01  (step t293.t3 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t293.t2 t293.a0))
% 6.76/7.01  (step t293 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule subproof :discharge (t293.a0))
% 6.76/7.01  (step t294 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t292 t293))
% 6.76/7.01  (step t295 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))))) :rule implies_neg2)
% 6.76/7.01  (step t296 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))))) :rule resolution :premises (t294 t295))
% 6.76/7.01  (step t297 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity))))) :rule contraction :premises (t296))
% 6.76/7.01  (step t298 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule implies :premises (t297))
% 6.76/7.01  (step t299 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.a))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t298 a17))
% 6.76/7.01  (step t300 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t301)
% 6.76/7.01  (assume t301.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t301.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.inverse tptp.c))))
% 6.76/7.01  (step t301.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule or :premises (t301.t1))
% 6.76/7.01  (step t301.t3 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t301.t2 t301.a0))
% 6.76/7.01  (step t301 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule subproof :discharge (t301.a0))
% 6.76/7.01  (step t302 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t300 t301))
% 6.76/7.01  (step t303 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))))) :rule implies_neg2)
% 6.76/7.01  (step t304 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))))) :rule resolution :premises (t302 t303))
% 6.76/7.01  (step t305 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity))))) :rule contraction :premises (t304))
% 6.76/7.01  (step t306 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule implies :premises (t305))
% 6.76/7.01  (step t307 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.identity)))) :rule resolution :premises (t306 a17))
% 6.76/7.01  (step t308 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t309)
% 6.76/7.01  (assume t309.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t309.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))
% 6.76/7.01  (step t309.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule or :premises (t309.t1))
% 6.76/7.01  (step t309.t3 (cl (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule resolution :premises (t309.t2 t309.a0))
% 6.76/7.01  (step t309 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule subproof :discharge (t309.a0))
% 6.76/7.01  (step t310 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule resolution :premises (t308 t309))
% 6.76/7.01  (step t311 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (not (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t312 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))))) :rule resolution :premises (t310 t311))
% 6.76/7.01  (step t313 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a))))) :rule contraction :premises (t312))
% 6.76/7.01  (step t314 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule implies :premises (t313))
% 6.76/7.01  (step t315 (cl (= (tptp.inverse (tptp.multiply tptp.a (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.a)))) :rule resolution :premises (t314 a17))
% 6.76/7.01  (step t316 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t317)
% 6.76/7.01  (assume t317.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t317.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (:= Y (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t317.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule or :premises (t317.t1))
% 6.76/7.01  (step t317.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t317.t2 t317.a0))
% 6.76/7.01  (step t317 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule subproof :discharge (t317.a0))
% 6.76/7.01  (step t318 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t316 t317))
% 6.76/7.01  (step t319 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t320 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule resolution :premises (t318 t319))
% 6.76/7.01  (step t321 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule contraction :premises (t320))
% 6.76/7.01  (step t322 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule implies :premises (t321))
% 6.76/7.01  (step t323 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t322 a17))
% 6.76/7.01  (step t324 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t325)
% 6.76/7.01  (assume t325.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t325.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (:= Y (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))
% 6.76/7.01  (step t325.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule or :premises (t325.t1))
% 6.76/7.01  (step t325.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule resolution :premises (t325.t2 t325.a0))
% 6.76/7.01  (step t325 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule subproof :discharge (t325.a0))
% 6.76/7.01  (step t326 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule resolution :premises (t324 t325))
% 6.76/7.01  (step t327 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t328 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))) :rule resolution :premises (t326 t327))
% 6.76/7.01  (step t329 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))) :rule contraction :premises (t328))
% 6.76/7.01  (step t330 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule implies :premises (t329))
% 6.76/7.01  (step t331 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule resolution :premises (t330 a17))
% 6.76/7.01  (step t332 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t333)
% 6.76/7.01  (assume t333.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t333.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.c)) (:= Y (tptp.inverse tptp.c))))
% 6.76/7.01  (step t333.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule or :premises (t333.t1))
% 6.76/7.01  (step t333.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t333.t2 t333.a0))
% 6.76/7.01  (step t333 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule subproof :discharge (t333.a0))
% 6.76/7.01  (step t334 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t332 t333))
% 6.76/7.01  (step t335 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t336 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t334 t335))
% 6.76/7.01  (step t337 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule contraction :premises (t336))
% 6.76/7.01  (step t338 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies :premises (t337))
% 6.76/7.01  (step t339 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c))) (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t338 a17))
% 6.76/7.01  (step t340 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t341)
% 6.76/7.01  (assume t341.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t341.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (:= Y tptp.identity)))
% 6.76/7.01  (step t341.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule or :premises (t341.t1))
% 6.76/7.01  (step t341.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule resolution :premises (t341.t2 t341.a0))
% 6.76/7.01  (step t341 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule subproof :discharge (t341.a0))
% 6.76/7.01  (step t342 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule resolution :premises (t340 t341))
% 6.76/7.01  (step t343 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t344 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))) :rule resolution :premises (t342 t343))
% 6.76/7.01  (step t345 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)))))) :rule contraction :premises (t344))
% 6.76/7.01  (step t346 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule implies :premises (t345))
% 6.76/7.01  (step t347 (cl (= (tptp.inverse (tptp.multiply (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c) tptp.identity)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c))))) :rule resolution :premises (t346 a17))
% 6.76/7.01  (step t348 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t349)
% 6.76/7.01  (assume t349.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 6.76/7.01  (step t349.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t349.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule or :premises (t349.t1))
% 6.76/7.01  (step t349.t3 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t349.t2 t349.a0))
% 6.76/7.01  (step t349 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule subproof :discharge (t349.a0))
% 6.76/7.01  (step t350 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t348 t349))
% 6.76/7.01  (step t351 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t352 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t350 t351))
% 6.76/7.01  (step t353 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule contraction :premises (t352))
% 6.76/7.01  (step t354 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies :premises (t353))
% 6.76/7.01  (step t355 (cl (= (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t354 t167))
% 6.76/7.01  (step t356 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t357)
% 6.76/7.01  (assume t357.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t357.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule forall_inst :args ((:= Y (tptp.inverse tptp.c)) (:= Z (tptp.inverse tptp.a)) (:= X tptp.a)))
% 6.76/7.01  (step t357.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule or :premises (t357.t1))
% 6.76/7.01  (step t357.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t357.t2 t357.a0))
% 6.76/7.01  (step t357 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule subproof :discharge (t357.a0))
% 6.76/7.01  (step t358 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t356 t357))
% 6.76/7.01  (step t359 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t360 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule resolution :premises (t358 t359))
% 6.76/7.01  (step t361 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a))))) :rule contraction :premises (t360))
% 6.76/7.01  (step t362 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies :premises (t361))
% 6.76/7.01  (step t363 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)) tptp.a) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t362 a14))
% 6.76/7.01  (step t364 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t365)
% 6.76/7.01  (assume t365.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t365.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= Y (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))) (:= Z (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (:= X (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t365.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule or :premises (t365.t1))
% 6.76/7.01  (step t365.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t365.t2 t365.a0))
% 6.76/7.01  (step t365 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule subproof :discharge (t365.a0))
% 6.76/7.01  (step t366 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t364 t365))
% 6.76/7.01  (step t367 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t368 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t366 t367))
% 6.76/7.01  (step t369 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule contraction :premises (t368))
% 6.76/7.01  (step t370 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies :premises (t369))
% 6.76/7.01  (step t371 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t370 a14))
% 6.76/7.01  (step t372 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t373)
% 6.76/7.01  (assume t373.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t373.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))))) :rule forall_inst :args ((:= Y tptp.a) (:= Z tptp.c) (:= X (tptp.inverse tptp.c))))
% 6.76/7.01  (step t373.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule or :premises (t373.t1))
% 6.76/7.01  (step t373.t3 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule resolution :premises (t373.t2 t373.a0))
% 6.76/7.01  (step t373 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule subproof :discharge (t373.a0))
% 6.76/7.01  (step t374 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule resolution :premises (t372 t373))
% 6.76/7.01  (step t375 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (not (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t376 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))))) :rule resolution :premises (t374 t375))
% 6.76/7.01  (step t377 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c)))))) :rule contraction :premises (t376))
% 6.76/7.01  (step t378 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule implies :premises (t377))
% 6.76/7.01  (step t379 (cl (= (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.multiply tptp.a (tptp.inverse tptp.c)) (tptp.multiply tptp.c (tptp.inverse tptp.c))))) :rule resolution :premises (t378 a13))
% 6.76/7.01  (step t380 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t381)
% 6.76/7.01  (assume t381.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t381.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= Y (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (:= X (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t381.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule or :premises (t381.t1))
% 6.76/7.01  (step t381.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t381.t2 t381.a0))
% 6.76/7.01  (step t381 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule subproof :discharge (t381.a0))
% 6.76/7.01  (step t382 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t380 t381))
% 6.76/7.01  (step t383 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t384 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t382 t383))
% 6.76/7.01  (step t385 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule contraction :premises (t384))
% 6.76/7.01  (step t386 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies :premises (t385))
% 6.76/7.01  (step t387 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t386 a13))
% 6.76/7.01  (step t388 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t389)
% 6.76/7.01  (assume t389.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t389.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= Y (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (:= X (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t389.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule or :premises (t389.t1))
% 6.76/7.01  (step t389.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t389.t2 t389.a0))
% 6.76/7.01  (step t389 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule subproof :discharge (t389.a0))
% 6.76/7.01  (step t390 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t388 t389))
% 6.76/7.01  (step t391 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t392 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule resolution :premises (t390 t391))
% 6.76/7.01  (step t393 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule contraction :premises (t392))
% 6.76/7.01  (step t394 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule implies :premises (t393))
% 6.76/7.01  (step t395 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t394 a13))
% 6.76/7.01  (step t396 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t397)
% 6.76/7.01  (assume t397.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t397.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))))) :rule forall_inst :args ((:= Y (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= X tptp.c)))
% 6.76/7.01  (step t397.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) :rule or :premises (t397.t1))
% 6.76/7.01  (step t397.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) :rule resolution :premises (t397.t2 t397.a0))
% 6.76/7.01  (step t397 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) :rule subproof :discharge (t397.a0))
% 6.76/7.01  (step t398 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) :rule resolution :premises (t396 t397))
% 6.76/7.01  (step t399 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t400 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))))) :rule resolution :premises (t398 t399))
% 6.76/7.01  (step t401 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c))))) :rule contraction :premises (t400))
% 6.76/7.01  (step t402 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) :rule implies :premises (t401))
% 6.76/7.01  (step t403 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.c) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c) (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.c)))) :rule resolution :premises (t402 a13))
% 6.76/7.01  (step t404 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t405)
% 6.76/7.01  (assume t405.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t405.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.c)) (:= Y (tptp.inverse tptp.c)) (:= Z (tptp.least_upper_bound tptp.c tptp.a))))
% 6.76/7.01  (step t405.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule or :premises (t405.t1))
% 6.76/7.01  (step t405.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule resolution :premises (t405.t2 t405.a0))
% 6.76/7.01  (step t405 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule subproof :discharge (t405.a0))
% 6.76/7.01  (step t406 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule resolution :premises (t404 t405))
% 6.76/7.01  (step t407 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t408 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))))) :rule resolution :premises (t406 t407))
% 6.76/7.01  (step t409 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))))) :rule contraction :premises (t408))
% 6.76/7.01  (step t410 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule implies :premises (t409))
% 6.76/7.01  (step t411 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse tptp.c)) (tptp.least_upper_bound tptp.c tptp.a)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.c tptp.a))))) :rule resolution :premises (t410 a2))
% 6.76/7.01  (step t412 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t413)
% 6.76/7.01  (assume t413.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t413.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (:= Z (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t413.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule or :premises (t413.t1))
% 6.76/7.01  (step t413.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t413.t2 t413.a0))
% 6.76/7.01  (step t413 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule subproof :discharge (t413.a0))
% 6.76/7.01  (step t414 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t412 t413))
% 6.76/7.01  (step t415 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t416 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t414 t415))
% 6.76/7.01  (step t417 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule contraction :premises (t416))
% 6.76/7.01  (step t418 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies :premises (t417))
% 6.76/7.01  (step t419 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.a) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t418 a2))
% 6.76/7.01  (step t420 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t421)
% 6.76/7.01  (assume t421.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t421.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.identity)) (:= Y (tptp.inverse (tptp.inverse tptp.b))) (:= Z (tptp.inverse tptp.b))))
% 6.76/7.01  (step t421.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule or :premises (t421.t1))
% 6.76/7.01  (step t421.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule resolution :premises (t421.t2 t421.a0))
% 6.76/7.01  (step t421 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule subproof :discharge (t421.a0))
% 6.76/7.01  (step t422 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule resolution :premises (t420 t421))
% 6.76/7.01  (step t423 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))))) :rule implies_neg2)
% 6.76/7.01  (step t424 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))))) :rule resolution :premises (t422 t423))
% 6.76/7.01  (step t425 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))))) :rule contraction :premises (t424))
% 6.76/7.01  (step t426 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule implies :premises (t425))
% 6.76/7.01  (step t427 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.inverse tptp.b))) (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule resolution :premises (t426 a2))
% 6.76/7.01  (step t428 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t429)
% 6.76/7.01  (assume t429.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t429.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.b))) (:= Y (tptp.inverse tptp.b)) (:= Z (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t429.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule or :premises (t429.t1))
% 6.76/7.01  (step t429.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t429.t2 t429.a0))
% 6.76/7.01  (step t429 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule subproof :discharge (t429.a0))
% 6.76/7.01  (step t430 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t428 t429))
% 6.76/7.01  (step t431 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t432 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t430 t431))
% 6.76/7.01  (step t433 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule contraction :premises (t432))
% 6.76/7.01  (step t434 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies :premises (t433))
% 6.76/7.01  (step t435 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t434 a2))
% 6.76/7.01  (step t436 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t437)
% 6.76/7.01  (assume t437.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t437.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Y (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z tptp.b)))
% 6.76/7.01  (step t437.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule or :premises (t437.t1))
% 6.76/7.01  (step t437.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule resolution :premises (t437.t2 t437.a0))
% 6.76/7.01  (step t437 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule subproof :discharge (t437.a0))
% 6.76/7.01  (step t438 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule resolution :premises (t436 t437))
% 6.76/7.01  (step t439 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule implies_neg2)
% 6.76/7.01  (step t440 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule resolution :premises (t438 t439))
% 6.76/7.01  (step t441 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b))))) :rule contraction :premises (t440))
% 6.76/7.01  (step t442 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule implies :premises (t441))
% 6.76/7.01  (step t443 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.b) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.b)))) :rule resolution :premises (t442 a2))
% 6.76/7.01  (step t444 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t445)
% 6.76/7.01  (assume t445.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t445.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Y (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z tptp.a)))
% 6.76/7.01  (step t445.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule or :premises (t445.t1))
% 6.76/7.01  (step t445.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule resolution :premises (t445.t2 t445.a0))
% 6.76/7.01  (step t445 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule subproof :discharge (t445.a0))
% 6.76/7.01  (step t446 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule resolution :premises (t444 t445))
% 6.76/7.01  (step t447 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t448 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule resolution :premises (t446 t447))
% 6.76/7.01  (step t449 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a))))) :rule contraction :premises (t448))
% 6.76/7.01  (step t450 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule implies :premises (t449))
% 6.76/7.01  (step t451 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) tptp.a) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) tptp.a)))) :rule resolution :premises (t450 a2))
% 6.76/7.01  (step t452 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t453)
% 6.76/7.01  (assume t453.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 6.76/7.01  (step t453.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t453.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule or :premises (t453.t1))
% 6.76/7.01  (step t453.t3 (cl (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t453.t2 t453.a0))
% 6.76/7.01  (step t453 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule subproof :discharge (t453.a0))
% 6.76/7.01  (step t454 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t452 t453))
% 6.76/7.01  (step t455 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t456 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t454 t455))
% 6.76/7.01  (step t457 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule contraction :premises (t456))
% 6.76/7.01  (step t458 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies :premises (t457))
% 6.76/7.01  (step t459 (cl (= (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t458 t266))
% 6.76/7.01  (step t460 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t461)
% 6.76/7.01  (assume t461.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 6.76/7.01  (step t461.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t461.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule or :premises (t461.t1))
% 6.76/7.01  (step t461.t3 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule resolution :premises (t461.t2 t461.a0))
% 6.76/7.01  (step t461 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule subproof :discharge (t461.a0))
% 6.76/7.01  (step t462 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule resolution :premises (t460 t461))
% 6.76/7.01  (step t463 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t464 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t462 t463))
% 6.76/7.01  (step t465 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule contraction :premises (t464))
% 6.76/7.01  (step t466 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule implies :premises (t465))
% 6.76/7.01  (step t467 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule resolution :premises (t466 t266))
% 6.76/7.01  (step t468 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t469)
% 6.76/7.01  (assume t469.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t469.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (:= Y (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t469.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule or :premises (t469.t1))
% 6.76/7.01  (step t469.t3 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t469.t2 t469.a0))
% 6.76/7.01  (step t469 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule subproof :discharge (t469.a0))
% 6.76/7.01  (step t470 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t468 t469))
% 6.76/7.01  (step t471 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t472 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule resolution :premises (t470 t471))
% 6.76/7.01  (step t473 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))))) :rule contraction :premises (t472))
% 6.76/7.01  (step t474 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule implies :premises (t473))
% 6.76/7.01  (step t475 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))) (tptp.greatest_lower_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t474 a21))
% 6.76/7.01  (step t476 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t477)
% 6.76/7.01  (assume t477.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t477.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (:= Y (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t477.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule or :premises (t477.t1))
% 6.76/7.01  (step t477.t3 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t477.t2 t477.a0))
% 6.76/7.01  (step t477 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule subproof :discharge (t477.a0))
% 6.76/7.01  (step t478 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t476 t477))
% 6.76/7.01  (step t479 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t480 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t478 t479))
% 6.76/7.01  (step t481 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))))) :rule contraction :premises (t480))
% 6.76/7.01  (step t482 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies :premises (t481))
% 6.76/7.01  (step t483 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t482 a20))
% 6.76/7.01  (step t484 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t485)
% 6.76/7.01  (assume t485.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t485.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.b)) (:= Y (tptp.greatest_lower_bound tptp.a tptp.c))))
% 6.76/7.01  (step t485.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule or :premises (t485.t1))
% 6.76/7.01  (step t485.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule resolution :premises (t485.t2 t485.a0))
% 6.76/7.01  (step t485 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule subproof :discharge (t485.a0))
% 6.76/7.01  (step t486 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule resolution :premises (t484 t485))
% 6.76/7.01  (step t487 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))) :rule implies_neg2)
% 6.76/7.01  (step t488 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))) :rule resolution :premises (t486 t487))
% 6.76/7.01  (step t489 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))) :rule contraction :premises (t488))
% 6.76/7.01  (step t490 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule implies :premises (t489))
% 6.76/7.01  (step t491 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule resolution :premises (t490 a17))
% 6.76/7.01  (step t492 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t493)
% 6.76/7.01  (assume t493.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t493.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.b)) (:= Y (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t493.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule or :premises (t493.t1))
% 6.76/7.01  (step t493.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule resolution :premises (t493.t2 t493.a0))
% 6.76/7.01  (step t493 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule subproof :discharge (t493.a0))
% 6.76/7.01  (step t494 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule resolution :premises (t492 t493))
% 6.76/7.01  (step t495 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))) :rule implies_neg2)
% 6.76/7.01  (step t496 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))) :rule resolution :premises (t494 t495))
% 6.76/7.01  (step t497 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b)))))) :rule contraction :premises (t496))
% 6.76/7.01  (step t498 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule implies :premises (t497))
% 6.76/7.01  (step t499 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.b))))) :rule resolution :premises (t498 a17))
% 6.76/7.01  (step t500 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t501)
% 6.76/7.01  (assume t501.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t501.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.c)) (:= Y (tptp.greatest_lower_bound tptp.a tptp.c))))
% 6.76/7.01  (step t501.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule or :premises (t501.t1))
% 6.76/7.01  (step t501.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t501.t2 t501.a0))
% 6.76/7.01  (step t501 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule subproof :discharge (t501.a0))
% 6.76/7.01  (step t502 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t500 t501))
% 6.76/7.01  (step t503 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t504 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule resolution :premises (t502 t503))
% 6.76/7.01  (step t505 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule contraction :premises (t504))
% 6.76/7.01  (step t506 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule implies :premises (t505))
% 6.76/7.01  (step t507 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t506 a17))
% 6.76/7.01  (step t508 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t509)
% 6.76/7.01  (assume t509.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t509.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (:= Y tptp.c)))
% 6.76/7.01  (step t509.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule or :premises (t509.t1))
% 6.76/7.01  (step t509.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t509.t2 t509.a0))
% 6.76/7.01  (step t509 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule subproof :discharge (t509.a0))
% 6.76/7.01  (step t510 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t508 t509))
% 6.76/7.01  (step t511 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t512 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule resolution :premises (t510 t511))
% 6.76/7.01  (step t513 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule contraction :premises (t512))
% 6.76/7.01  (step t514 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule implies :premises (t513))
% 6.76/7.01  (step t515 (cl (= (tptp.inverse (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t514 a17))
% 6.76/7.01  (step t516 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t517)
% 6.76/7.01  (assume t517.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t517.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t517.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule or :premises (t517.t1))
% 6.76/7.01  (step t517.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t517.t2 t517.a0))
% 6.76/7.01  (step t517 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t517.a0))
% 6.76/7.01  (step t518 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t516 t517))
% 6.76/7.01  (step t519 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t520 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t518 t519))
% 6.76/7.01  (step t521 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t520))
% 6.76/7.01  (step t522 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t521))
% 6.76/7.01  (step t523 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.a) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t522 a17))
% 6.76/7.01  (step t524 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t525)
% 6.76/7.01  (assume t525.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t525.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.c)) (:= Y (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t525.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule or :premises (t525.t1))
% 6.76/7.01  (step t525.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t525.t2 t525.a0))
% 6.76/7.01  (step t525 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule subproof :discharge (t525.a0))
% 6.76/7.01  (step t526 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t524 t525))
% 6.76/7.01  (step t527 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t528 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule resolution :premises (t526 t527))
% 6.76/7.01  (step t529 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule contraction :premises (t528))
% 6.76/7.01  (step t530 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule implies :premises (t529))
% 6.76/7.01  (step t531 (cl (= (tptp.inverse (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t530 a17))
% 6.76/7.01  (step t532 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t533)
% 6.76/7.01  (assume t533.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t533.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (:= Y tptp.c)))
% 6.76/7.01  (step t533.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule or :premises (t533.t1))
% 6.76/7.01  (step t533.t3 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t533.t2 t533.a0))
% 6.76/7.01  (step t533 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule subproof :discharge (t533.a0))
% 6.76/7.01  (step t534 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t532 t533))
% 6.76/7.01  (step t535 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (not (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t536 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule resolution :premises (t534 t535))
% 6.76/7.01  (step t537 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))))) :rule contraction :premises (t536))
% 6.76/7.01  (step t538 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule implies :premises (t537))
% 6.76/7.01  (step t539 (cl (= (tptp.inverse (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) tptp.c)) (tptp.multiply (tptp.inverse tptp.c) (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t538 a17))
% 6.76/7.01  (step t540 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t541)
% 6.76/7.01  (assume t541.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))))
% 6.76/7.01  (step t541.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))
% 6.76/7.01  (step t541.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule or :premises (t541.t1))
% 6.76/7.01  (step t541.t3 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule resolution :premises (t541.t2 t541.a0))
% 6.76/7.01  (step t541 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule subproof :discharge (t541.a0))
% 6.76/7.01  (step t542 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule resolution :premises (t540 t541))
% 6.76/7.01  (step t543 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (not (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))))) :rule implies_neg2)
% 6.76/7.01  (step t544 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))))) :rule resolution :premises (t542 t543))
% 6.76/7.01  (step t545 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X)))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity))))) :rule contraction :premises (t544))
% 6.76/7.01  (step t546 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.multiply X Y)) (tptp.multiply (tptp.inverse Y) (tptp.inverse X))))) (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule implies :premises (t545))
% 6.76/7.01  (step t547 (cl (= (tptp.inverse (tptp.multiply tptp.identity (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.inverse tptp.identity)))) :rule resolution :premises (t546 a17))
% 6.76/7.01  (step t548 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t549)
% 6.76/7.01  (assume t549.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t549.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= Y (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c))) (:= Z (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (:= X (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t549.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule or :premises (t549.t1))
% 6.76/7.01  (step t549.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t549.t2 t549.a0))
% 6.76/7.01  (step t549 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule subproof :discharge (t549.a0))
% 6.76/7.01  (step t550 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t548 t549))
% 6.76/7.01  (step t551 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t552 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t550 t551))
% 6.76/7.01  (step t553 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule contraction :premises (t552))
% 6.76/7.01  (step t554 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies :premises (t553))
% 6.76/7.01  (step t555 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound (tptp.multiply (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t554 a13))
% 6.76/7.01  (step t556 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t557)
% 6.76/7.01  (assume t557.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))))
% 6.76/7.01  (step t557.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.c)) (:= Y tptp.a) (:= Z tptp.c)))
% 6.76/7.01  (step t557.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule or :premises (t557.t1))
% 6.76/7.01  (step t557.t3 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule resolution :premises (t557.t2 t557.a0))
% 6.76/7.01  (step t557 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule subproof :discharge (t557.a0))
% 6.76/7.01  (step t558 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule resolution :premises (t556 t557))
% 6.76/7.01  (step t559 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (not (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t560 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))))) :rule resolution :premises (t558 t559))
% 6.76/7.01  (step t561 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z)))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c))))) :rule contraction :premises (t560))
% 6.76/7.01  (step t562 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.greatest_lower_bound Y Z)) (tptp.greatest_lower_bound (tptp.multiply X Y) (tptp.multiply X Z))))) (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule implies :premises (t561))
% 6.76/7.01  (step t563 (cl (= (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) tptp.a) (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule resolution :premises (t562 a12))
% 6.76/7.01  (step t564 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t565)
% 6.76/7.01  (assume t565.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t565.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.c)) (:= Y (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Z (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t565.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule or :premises (t565.t1))
% 6.76/7.01  (step t565.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t565.t2 t565.a0))
% 6.76/7.01  (step t565 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule subproof :discharge (t565.a0))
% 6.76/7.01  (step t566 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t564 t565))
% 6.76/7.01  (step t567 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t568 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t566 t567))
% 6.76/7.01  (step t569 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule contraction :premises (t568))
% 6.76/7.01  (step t570 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies :premises (t569))
% 6.76/7.01  (step t571 (cl (= (tptp.multiply (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t570 a2))
% 6.76/7.01  (step t572 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t573)
% 6.76/7.01  (assume t573.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t573.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule forall_inst :args ((:= X (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))) (:= Y (tptp.least_upper_bound tptp.a tptp.c)) (:= Z (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t573.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule or :premises (t573.t1))
% 6.76/7.01  (step t573.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t573.t2 t573.a0))
% 6.76/7.01  (step t573 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule subproof :discharge (t573.a0))
% 6.76/7.01  (step t574 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t572 t573))
% 6.76/7.01  (step t575 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (not (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule implies_neg2)
% 6.76/7.01  (step t576 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule resolution :premises (t574 t575))
% 6.76/7.01  (step t577 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))))) :rule contraction :premises (t576))
% 6.76/7.01  (step t578 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies :premises (t577))
% 6.76/7.01  (step t579 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.multiply (tptp.least_upper_bound tptp.a tptp.c) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t578 a2))
% 6.76/7.01  (step t580 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t581)
% 6.76/7.01  (assume t581.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 6.76/7.01  (step t581.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))
% 6.76/7.01  (step t581.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule or :premises (t581.t1))
% 6.76/7.01  (step t581.t3 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t581.t2 t581.a0))
% 6.76/7.01  (step t581 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule subproof :discharge (t581.a0))
% 6.76/7.01  (step t582 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t580 t581))
% 6.76/7.01  (step t583 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t584 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t582 t583))
% 6.76/7.01  (step t585 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)))))) :rule contraction :premises (t584))
% 6.76/7.01  (step t586 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies :premises (t585))
% 6.76/7.01  (step t587 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply tptp.identity (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t586 t266))
% 6.76/7.01  (step t588 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t589)
% 6.76/7.01  (assume t589.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t589.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.b tptp.c)) (:= Y tptp.c)))
% 6.76/7.01  (step t589.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule or :premises (t589.t1))
% 6.76/7.01  (step t589.t3 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule resolution :premises (t589.t2 t589.a0))
% 6.76/7.01  (step t589 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule subproof :discharge (t589.a0))
% 6.76/7.01  (step t590 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule resolution :premises (t588 t589))
% 6.76/7.01  (step t591 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t592 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))))) :rule resolution :premises (t590 t591))
% 6.76/7.01  (step t593 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c))))) :rule contraction :premises (t592))
% 6.76/7.01  (step t594 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule implies :premises (t593))
% 6.76/7.01  (step t595 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c)) (tptp.greatest_lower_bound (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.inverse tptp.c)))) :rule resolution :premises (t594 a21))
% 6.76/7.01  (step t596 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t597)
% 6.76/7.01  (assume t597.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 6.76/7.01  (step t597.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))))) :rule forall_inst :args ((:= X tptp.b)))
% 6.76/7.01  (step t597.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) :rule or :premises (t597.t1))
% 6.76/7.01  (step t597.t3 (cl (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) :rule resolution :premises (t597.t2 t597.a0))
% 6.76/7.01  (step t597 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) :rule subproof :discharge (t597.a0))
% 6.76/7.01  (step t598 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) :rule resolution :premises (t596 t597))
% 6.76/7.01  (step t599 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (not (= tptp.b (tptp.inverse (tptp.inverse tptp.b))))) :rule implies_neg2)
% 6.76/7.01  (step t600 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))))) :rule resolution :premises (t598 t599))
% 6.76/7.01  (step t601 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b))))) :rule contraction :premises (t600))
% 6.76/7.01  (step t602 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) :rule implies :premises (t601))
% 6.76/7.01  (step t603 (cl (= tptp.b (tptp.inverse (tptp.inverse tptp.b)))) :rule resolution :premises (t602 t167))
% 6.76/7.01  (step t604 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t605)
% 6.76/7.01  (assume t605.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 6.76/7.01  (step t605.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 6.76/7.01  (step t605.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule or :premises (t605.t1))
% 6.76/7.01  (step t605.t3 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t605.t2 t605.a0))
% 6.76/7.01  (step t605 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule subproof :discharge (t605.a0))
% 6.76/7.01  (step t606 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t604 t605))
% 6.76/7.01  (step t607 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (not (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t608 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t606 t607))
% 6.76/7.01  (step t609 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a))))) :rule contraction :premises (t608))
% 6.76/7.01  (step t610 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule implies :premises (t609))
% 6.76/7.01  (step t611 (cl (= tptp.a (tptp.inverse (tptp.inverse tptp.a)))) :rule resolution :premises (t610 t167))
% 6.76/7.01  (step t612 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t613)
% 6.76/7.01  (assume t613.a0 (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))))
% 6.76/7.01  (step t613.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X tptp.c)))
% 6.76/7.01  (step t613.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule or :premises (t613.t1))
% 6.76/7.01  (step t613.t3 (cl (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule resolution :premises (t613.t2 t613.a0))
% 6.76/7.01  (step t613 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule subproof :discharge (t613.a0))
% 6.76/7.01  (step t614 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule resolution :premises (t612 t613))
% 6.76/7.01  (step t615 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (not (= tptp.c (tptp.inverse (tptp.inverse tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t616 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t614 t615))
% 6.76/7.01  (step t617 (cl (=> (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X)))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c))))) :rule contraction :premises (t616))
% 6.76/7.01  (step t618 (cl (not (forall ((X $$unsorted)) (= X (tptp.inverse (tptp.inverse X))))) (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule implies :premises (t617))
% 6.76/7.01  (step t619 (cl (= tptp.c (tptp.inverse (tptp.inverse tptp.c)))) :rule resolution :premises (t618 t167))
% 6.76/7.01  (step t620 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t621)
% 6.76/7.01  (assume t621.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t621.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= Y (tptp.inverse tptp.c)) (:= Z (tptp.inverse tptp.b)) (:= X (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t621.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule or :premises (t621.t1))
% 6.76/7.01  (step t621.t3 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t621.t2 t621.a0))
% 6.76/7.01  (step t621 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule subproof :discharge (t621.a0))
% 6.76/7.01  (step t622 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t620 t621))
% 6.76/7.01  (step t623 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t624 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t622 t623))
% 6.76/7.01  (step t625 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule contraction :premises (t624))
% 6.76/7.01  (step t626 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.greatest_lower_bound Y Z) X) (tptp.greatest_lower_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies :premises (t625))
% 6.76/7.01  (step t627 (cl (= (tptp.multiply (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t626 a14))
% 6.76/7.01  (step t628 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t629)
% 6.76/7.01  (assume t629.a0 (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))))
% 6.76/7.01  (step t629.t1 (cl (or (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= Y (tptp.inverse tptp.c)) (:= Z (tptp.inverse tptp.b)) (:= X (tptp.greatest_lower_bound tptp.a tptp.c))))
% 6.76/7.01  (step t629.t2 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule or :premises (t629.t1))
% 6.76/7.01  (step t629.t3 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule resolution :premises (t629.t2 t629.a0))
% 6.76/7.01  (step t629 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule subproof :discharge (t629.a0))
% 6.76/7.01  (step t630 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule resolution :premises (t628 t629))
% 6.76/7.01  (step t631 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t632 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule resolution :premises (t630 t631))
% 6.76/7.01  (step t633 (cl (=> (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c)))))) :rule contraction :premises (t632))
% 6.76/7.01  (step t634 (cl (not (forall ((Y $$unsorted) (Z $$unsorted) (X $$unsorted)) (= (tptp.multiply (tptp.least_upper_bound Y Z) X) (tptp.least_upper_bound (tptp.multiply Y X) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule implies :premises (t633))
% 6.76/7.01  (step t635 (cl (= (tptp.multiply (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.multiply (tptp.inverse tptp.c) (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.b) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule resolution :premises (t634 a13))
% 6.76/7.01  (step t636 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t637)
% 6.76/7.01  (assume t637.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 6.76/7.01  (step t637.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.inverse (tptp.inverse tptp.c)))))
% 6.76/7.01  (step t637.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule or :premises (t637.t1))
% 6.76/7.01  (step t637.t3 (cl (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t637.t2 t637.a0))
% 6.76/7.01  (step t637 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t637.a0))
% 6.76/7.01  (step t638 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t636 t637))
% 6.76/7.01  (step t639 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t640 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t638 t639))
% 6.76/7.01  (step t641 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t640))
% 6.76/7.01  (step t642 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t641))
% 6.76/7.01  (step t643 (cl (= (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t642 a4))
% 6.76/7.01  (step t644 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t645)
% 6.76/7.01  (assume t645.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 6.76/7.01  (step t645.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.b tptp.c)) (:= Y tptp.c)))
% 6.76/7.01  (step t645.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule or :premises (t645.t1))
% 6.76/7.01  (step t645.t3 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule resolution :premises (t645.t2 t645.a0))
% 6.76/7.01  (step t645 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule subproof :discharge (t645.a0))
% 6.76/7.01  (step t646 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule resolution :premises (t644 t645))
% 6.76/7.01  (step t647 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (not (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t648 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))))) :rule resolution :premises (t646 t647))
% 6.76/7.01  (step t649 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c))))) :rule contraction :premises (t648))
% 6.76/7.01  (step t650 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule implies :premises (t649))
% 6.76/7.01  (step t651 (cl (= (tptp.least_upper_bound (tptp.greatest_lower_bound tptp.b tptp.c) tptp.c) (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.b tptp.c)))) :rule resolution :premises (t650 a4))
% 6.76/7.01  (step t652 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t653)
% 6.76/7.01  (assume t653.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 6.76/7.01  (step t653.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.inverse (tptp.inverse tptp.c)))))
% 6.76/7.01  (step t653.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule or :premises (t653.t1))
% 6.76/7.01  (step t653.t3 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t653.t2 t653.a0))
% 6.76/7.01  (step t653 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule subproof :discharge (t653.a0))
% 6.76/7.01  (step t654 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t652 t653))
% 6.76/7.01  (step t655 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (not (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule implies_neg2)
% 6.76/7.01  (step t656 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule resolution :premises (t654 t655))
% 6.76/7.01  (step t657 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a)))))) :rule contraction :premises (t656))
% 6.76/7.01  (step t658 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule implies :premises (t657))
% 6.76/7.01  (step t659 (cl (= (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse (tptp.inverse tptp.a))))) :rule resolution :premises (t658 a3))
% 6.76/7.01  (step t660 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t661)
% 6.76/7.01  (assume t661.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))))
% 6.76/7.01  (step t661.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.identity)) (:= Y (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (:= Z (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t661.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule or :premises (t661.t1))
% 6.76/7.01  (step t661.t3 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t661.t2 t661.a0))
% 6.76/7.01  (step t661 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule subproof :discharge (t661.a0))
% 6.76/7.01  (step t662 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t660 t661))
% 6.76/7.01  (step t663 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (not (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t664 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule resolution :premises (t662 t663))
% 6.76/7.01  (step t665 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z)))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))))) :rule contraction :premises (t664))
% 6.76/7.01  (step t666 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply (tptp.multiply X Y) Z) (tptp.multiply X (tptp.multiply Y Z))))) (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies :premises (t665))
% 6.76/7.01  (step t667 (cl (= (tptp.multiply (tptp.multiply (tptp.inverse tptp.identity) (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c))) (tptp.least_upper_bound tptp.a tptp.c)) (tptp.multiply (tptp.inverse tptp.identity) (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t666 a2))
% 6.76/7.01  (step t668 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t669)
% 6.76/7.01  (assume t669.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t669.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.b))))
% 6.76/7.01  (step t669.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule or :premises (t669.t1))
% 6.76/7.01  (step t669.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule resolution :premises (t669.t2 t669.a0))
% 6.76/7.01  (step t669 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule subproof :discharge (t669.a0))
% 6.76/7.01  (step t670 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule resolution :premises (t668 t669))
% 6.76/7.01  (step t671 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule implies_neg2)
% 6.76/7.01  (step t672 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule resolution :premises (t670 t671))
% 6.76/7.01  (step t673 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b))))) :rule contraction :premises (t672))
% 6.76/7.01  (step t674 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule implies :premises (t673))
% 6.76/7.01  (step t675 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) (not (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule equiv_pos2)
% 6.76/7.01  (anchor :step t676 :args ((X $$unsorted) (:= X X)))
% 6.76/7.01  (step t676.t1 (cl (= X X)) :rule refl)
% 6.76/7.01  (step t676.t2 (cl (= (= (tptp.multiply (tptp.inverse X) X) tptp.identity) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule all_simplify)
% 6.76/7.01  (step t676 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply (tptp.inverse X) X) tptp.identity)) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))) :rule bind)
% 6.76/7.01  (step t677 (cl (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule resolution :premises (t675 t676 a1))
% 6.76/7.01  (step t678 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.b)) (tptp.inverse tptp.b)))) :rule resolution :premises (t674 t677))
% 6.76/7.01  (step t679 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t680)
% 6.76/7.01  (assume t680.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t680.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a))))
% 6.76/7.01  (step t680.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule or :premises (t680.t1))
% 6.76/7.01  (step t680.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t680.t2 t680.a0))
% 6.76/7.01  (step t680 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule subproof :discharge (t680.a0))
% 6.76/7.01  (step t681 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t679 t680))
% 6.76/7.01  (step t682 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t683 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule resolution :premises (t681 t682))
% 6.76/7.01  (step t684 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a))))) :rule contraction :premises (t683))
% 6.76/7.01  (step t685 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule implies :premises (t684))
% 6.76/7.01  (step t686 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a)))) :rule resolution :premises (t685 t677))
% 6.76/7.01  (step t687 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t688)
% 6.76/7.01  (assume t688.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t688.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))
% 6.76/7.01  (step t688.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule or :premises (t688.t1))
% 6.76/7.01  (step t688.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule resolution :premises (t688.t2 t688.a0))
% 6.76/7.01  (step t688 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule subproof :discharge (t688.a0))
% 6.76/7.01  (step t689 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule resolution :premises (t687 t688))
% 6.76/7.01  (step t690 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t691 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule resolution :premises (t689 t690))
% 6.76/7.01  (step t692 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))))) :rule contraction :premises (t691))
% 6.76/7.01  (step t693 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule implies :premises (t692))
% 6.76/7.01  (step t694 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule resolution :premises (t693 t677))
% 6.76/7.01  (step t695 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t696)
% 6.76/7.01  (assume t696.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t696.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.c))))
% 6.76/7.01  (step t696.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule or :premises (t696.t1))
% 6.76/7.01  (step t696.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule resolution :premises (t696.t2 t696.a0))
% 6.76/7.01  (step t696 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule subproof :discharge (t696.a0))
% 6.76/7.01  (step t697 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule resolution :premises (t695 t696))
% 6.76/7.01  (step t698 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t699 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))) :rule resolution :premises (t697 t698))
% 6.76/7.01  (step t700 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c))))) :rule contraction :premises (t699))
% 6.76/7.01  (step t701 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule implies :premises (t700))
% 6.76/7.01  (step t702 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.inverse tptp.c)) (tptp.inverse tptp.c)))) :rule resolution :premises (t701 t677))
% 6.76/7.01  (step t703 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t704)
% 6.76/7.01  (assume t704.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t704.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.inverse tptp.c))))
% 6.76/7.01  (step t704.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule or :premises (t704.t1))
% 6.76/7.01  (step t704.t3 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t704.t2 t704.a0))
% 6.76/7.01  (step t704 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule subproof :discharge (t704.a0))
% 6.76/7.01  (step t705 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t703 t704))
% 6.76/7.01  (step t706 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t707 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule resolution :premises (t705 t706))
% 6.76/7.01  (step t708 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule contraction :premises (t707))
% 6.76/7.01  (step t709 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule implies :premises (t708))
% 6.76/7.01  (step t710 (cl (= (tptp.inverse (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.greatest_lower_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t709 a21))
% 6.76/7.01  (step t711 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t712)
% 6.76/7.01  (assume t712.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t712.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.inverse tptp.c))))
% 6.76/7.01  (step t712.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule or :premises (t712.t1))
% 6.76/7.01  (step t712.t3 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t712.t2 t712.a0))
% 6.76/7.01  (step t712 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule subproof :discharge (t712.a0))
% 6.76/7.01  (step t713 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t711 t712))
% 6.76/7.01  (step t714 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (not (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule implies_neg2)
% 6.76/7.01  (step t715 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule resolution :premises (t713 t714))
% 6.76/7.01  (step t716 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c)))))) :rule contraction :premises (t715))
% 6.76/7.01  (step t717 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule implies :premises (t716))
% 6.76/7.01  (step t718 (cl (= (tptp.inverse (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))) (tptp.least_upper_bound (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse (tptp.inverse tptp.c))))) :rule resolution :premises (t717 a20))
% 6.76/7.01  (step t719 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t720)
% 6.76/7.01  (assume t720.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))
% 6.76/7.01  (step t720.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))))) :rule forall_inst :args ((:= X tptp.c) (:= Y tptp.a)))
% 6.76/7.01  (step t720.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule or :premises (t720.t1))
% 6.76/7.01  (step t720.t3 (cl (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule resolution :premises (t720.t2 t720.a0))
% 6.76/7.01  (step t720 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule subproof :discharge (t720.a0))
% 6.76/7.01  (step t721 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule resolution :premises (t719 t720))
% 6.76/7.01  (step t722 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (not (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t723 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))))) :rule resolution :premises (t721 t722))
% 6.76/7.01  (step t724 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a))))) :rule contraction :premises (t723))
% 6.76/7.01  (step t725 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule implies :premises (t724))
% 6.76/7.01  (step t726 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule equiv_pos2)
% 6.76/7.01  (anchor :step t727 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 6.76/7.01  (step t727.t1 (cl (= X X)) :rule refl)
% 6.76/7.01  (step t727.t2 (cl (= Y Y)) :rule refl)
% 6.76/7.01  (step t727.t3 (cl (= (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule all_simplify)
% 6.76/7.01  (step t727 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y)))))) :rule bind)
% 6.76/7.01  (step t728 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.least_upper_bound X (tptp.greatest_lower_bound X Y))))) :rule resolution :premises (t726 t727 a9))
% 6.76/7.01  (step t729 (cl (= tptp.c (tptp.least_upper_bound tptp.c (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule resolution :premises (t725 t728))
% 6.76/7.01  (step t730 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t731)
% 6.76/7.01  (assume t731.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 6.76/7.01  (step t731.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.b)) (:= Y (tptp.inverse tptp.c))))
% 6.76/7.01  (step t731.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule or :premises (t731.t1))
% 6.76/7.01  (step t731.t3 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule resolution :premises (t731.t2 t731.a0))
% 6.76/7.01  (step t731 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule subproof :discharge (t731.a0))
% 6.76/7.01  (step t732 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule resolution :premises (t730 t731))
% 6.76/7.01  (step t733 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))) :rule implies_neg2)
% 6.76/7.01  (step t734 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))) :rule resolution :premises (t732 t733))
% 6.76/7.01  (step t735 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))) :rule contraction :premises (t734))
% 6.76/7.01  (step t736 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule implies :premises (t735))
% 6.76/7.01  (step t737 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule resolution :premises (t736 a4))
% 6.76/7.01  (step t738 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t739)
% 6.76/7.01  (assume t739.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 6.76/7.01  (step t739.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.inverse tptp.c))))
% 6.76/7.01  (step t739.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule or :premises (t739.t1))
% 6.76/7.01  (step t739.t3 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule resolution :premises (t739.t2 t739.a0))
% 6.76/7.01  (step t739 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule subproof :discharge (t739.a0))
% 6.76/7.01  (step t740 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule resolution :premises (t738 t739))
% 6.76/7.01  (step t741 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t742 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))) :rule resolution :premises (t740 t741))
% 6.76/7.01  (step t743 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))) :rule contraction :premises (t742))
% 6.76/7.01  (step t744 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule implies :premises (t743))
% 6.76/7.01  (step t745 (cl (= (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule resolution :premises (t744 a4))
% 6.76/7.01  (step t746 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t747)
% 6.76/7.01  (assume t747.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 6.76/7.01  (step t747.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.b)) (:= Y (tptp.inverse tptp.c))))
% 6.76/7.01  (step t747.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule or :premises (t747.t1))
% 6.76/7.01  (step t747.t3 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule resolution :premises (t747.t2 t747.a0))
% 6.76/7.01  (step t747 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule subproof :discharge (t747.a0))
% 6.76/7.01  (step t748 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule resolution :premises (t746 t747))
% 6.76/7.01  (step t749 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))) :rule implies_neg2)
% 6.76/7.01  (step t750 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))) :rule resolution :premises (t748 t749))
% 6.76/7.01  (step t751 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b))))) :rule contraction :premises (t750))
% 6.76/7.01  (step t752 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule implies :premises (t751))
% 6.76/7.01  (step t753 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.b)))) :rule resolution :premises (t752 a3))
% 6.76/7.01  (step t754 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t755)
% 6.76/7.01  (assume t755.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 6.76/7.01  (step t755.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X (tptp.inverse tptp.a)) (:= Y (tptp.inverse tptp.c))))
% 6.76/7.01  (step t755.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule or :premises (t755.t1))
% 6.76/7.01  (step t755.t3 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule resolution :premises (t755.t2 t755.a0))
% 6.76/7.01  (step t755 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule subproof :discharge (t755.a0))
% 6.76/7.01  (step t756 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule resolution :premises (t754 t755))
% 6.76/7.01  (step t757 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (not (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))) :rule implies_neg2)
% 6.76/7.01  (step t758 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))) :rule resolution :premises (t756 t757))
% 6.76/7.01  (step t759 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a))))) :rule contraction :premises (t758))
% 6.76/7.01  (step t760 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule implies :premises (t759))
% 6.76/7.01  (step t761 (cl (= (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.c) (tptp.inverse tptp.a)))) :rule resolution :premises (t760 a3))
% 6.76/7.01  (step t762 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t763)
% 6.76/7.01  (assume t763.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t763.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule forall_inst :args ((:= X (tptp.least_upper_bound tptp.a tptp.c))))
% 6.76/7.01  (step t763.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule or :premises (t763.t1))
% 6.76/7.01  (step t763.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule resolution :premises (t763.t2 t763.a0))
% 6.76/7.01  (step t763 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule subproof :discharge (t763.a0))
% 6.76/7.01  (step t764 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule resolution :premises (t762 t763))
% 6.76/7.01  (step t765 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t766 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t764 t765))
% 6.76/7.01  (step t767 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c))))) :rule contraction :premises (t766))
% 6.76/7.01  (step t768 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule implies :premises (t767))
% 6.76/7.01  (step t769 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.least_upper_bound tptp.a tptp.c)))) :rule resolution :premises (t768 t677))
% 6.76/7.01  (step t770 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t771)
% 6.76/7.01  (assume t771.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t771.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule forall_inst :args ((:= X (tptp.greatest_lower_bound tptp.a tptp.c))))
% 6.76/7.01  (step t771.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule or :premises (t771.t1))
% 6.76/7.01  (step t771.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule resolution :premises (t771.t2 t771.a0))
% 6.76/7.01  (step t771 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule subproof :discharge (t771.a0))
% 6.76/7.01  (step t772 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule resolution :premises (t770 t771))
% 6.76/7.01  (step t773 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (not (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t774 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule resolution :premises (t772 t773))
% 6.76/7.01  (step t775 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c))))) :rule contraction :premises (t774))
% 6.76/7.01  (step t776 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule implies :premises (t775))
% 6.76/7.01  (step t777 (cl (= tptp.identity (tptp.multiply (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.greatest_lower_bound tptp.a tptp.c)))) :rule resolution :premises (t776 t677))
% 6.76/7.01  (step t778 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t779)
% 6.76/7.01  (assume t779.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t779.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule forall_inst :args ((:= X tptp.b)))
% 6.76/7.01  (step t779.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule or :premises (t779.t1))
% 6.76/7.01  (step t779.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule resolution :premises (t779.t2 t779.a0))
% 6.76/7.01  (step t779 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule subproof :discharge (t779.a0))
% 6.76/7.01  (step t780 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule resolution :premises (t778 t779))
% 6.76/7.01  (step t781 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule implies_neg2)
% 6.76/7.01  (step t782 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule resolution :premises (t780 t781))
% 6.76/7.01  (step t783 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b)))) :rule contraction :premises (t782))
% 6.76/7.01  (step t784 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule implies :premises (t783))
% 6.76/7.01  (step t785 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.b) tptp.b))) :rule resolution :premises (t784 t677))
% 6.76/7.01  (step t786 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t787)
% 6.76/7.01  (assume t787.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t787.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule forall_inst :args ((:= X tptp.c)))
% 6.76/7.01  (step t787.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) :rule or :premises (t787.t1))
% 6.76/7.01  (step t787.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) :rule resolution :premises (t787.t2 t787.a0))
% 6.76/7.01  (step t787 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) :rule subproof :discharge (t787.a0))
% 6.76/7.01  (step t788 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) :rule resolution :premises (t786 t787))
% 6.76/7.01  (step t789 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule implies_neg2)
% 6.76/7.01  (step t790 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule resolution :premises (t788 t789))
% 6.76/7.01  (step t791 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c)))) :rule contraction :premises (t790))
% 6.76/7.01  (step t792 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) :rule implies :premises (t791))
% 6.76/7.01  (step t793 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.c) tptp.c))) :rule resolution :premises (t792 t677))
% 6.76/7.01  (step t794 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t795)
% 6.76/7.01  (assume t795.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t795.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule forall_inst :args ((:= X tptp.a)))
% 6.76/7.01  (step t795.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule or :premises (t795.t1))
% 6.76/7.01  (step t795.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t795.t2 t795.a0))
% 6.76/7.01  (step t795 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule subproof :discharge (t795.a0))
% 6.76/7.01  (step t796 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t794 t795))
% 6.76/7.01  (step t797 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule implies_neg2)
% 6.76/7.01  (step t798 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule resolution :premises (t796 t797))
% 6.76/7.01  (step t799 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a)))) :rule contraction :premises (t798))
% 6.76/7.01  (step t800 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule implies :premises (t799))
% 6.76/7.01  (step t801 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.a) tptp.a))) :rule resolution :premises (t800 t677))
% 6.76/7.01  (step t802 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t803)
% 6.76/7.01  (assume t803.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t803.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X tptp.b) (:= Y tptp.c)))
% 6.76/7.01  (step t803.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule or :premises (t803.t1))
% 6.76/7.01  (step t803.t3 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule resolution :premises (t803.t2 t803.a0))
% 6.76/7.01  (step t803 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule subproof :discharge (t803.a0))
% 6.76/7.01  (step t804 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule resolution :premises (t802 t803))
% 6.76/7.01  (step t805 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t806 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))) :rule resolution :premises (t804 t805))
% 6.76/7.01  (step t807 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))) :rule contraction :premises (t806))
% 6.76/7.01  (step t808 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule implies :premises (t807))
% 6.76/7.01  (step t809 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.b tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule resolution :premises (t808 a21))
% 6.76/7.01  (step t810 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t811)
% 6.76/7.01  (assume t811.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t811.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.c)))
% 6.76/7.01  (step t811.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule or :premises (t811.t1))
% 6.76/7.01  (step t811.t3 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule resolution :premises (t811.t2 t811.a0))
% 6.76/7.01  (step t811 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule subproof :discharge (t811.a0))
% 6.76/7.01  (step t812 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule resolution :premises (t810 t811))
% 6.76/7.01  (step t813 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t814 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule resolution :premises (t812 t813))
% 6.76/7.01  (step t815 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule contraction :premises (t814))
% 6.76/7.01  (step t816 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.least_upper_bound X Y)) (tptp.greatest_lower_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule implies :premises (t815))
% 6.76/7.01  (step t817 (cl (= (tptp.inverse (tptp.least_upper_bound tptp.a tptp.c)) (tptp.greatest_lower_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule resolution :premises (t816 a21))
% 6.76/7.01  (step t818 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t819)
% 6.76/7.01  (assume t819.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t819.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X tptp.b) (:= Y tptp.c)))
% 6.76/7.01  (step t819.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule or :premises (t819.t1))
% 6.76/7.01  (step t819.t3 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule resolution :premises (t819.t2 t819.a0))
% 6.76/7.01  (step t819 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule subproof :discharge (t819.a0))
% 6.76/7.01  (step t820 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule resolution :premises (t818 t819))
% 6.76/7.01  (step t821 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t822 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))) :rule resolution :premises (t820 t821))
% 6.76/7.01  (step t823 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c))))) :rule contraction :premises (t822))
% 6.76/7.01  (step t824 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule implies :premises (t823))
% 6.76/7.01  (step t825 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.b tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.b) (tptp.inverse tptp.c)))) :rule resolution :premises (t824 a20))
% 6.76/7.01  (step t826 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t827)
% 6.76/7.01  (assume t827.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))))
% 6.76/7.01  (step t827.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.c)))
% 6.76/7.01  (step t827.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule or :premises (t827.t1))
% 6.76/7.01  (step t827.t3 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule resolution :premises (t827.t2 t827.a0))
% 6.76/7.01  (step t827 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule subproof :discharge (t827.a0))
% 6.76/7.01  (step t828 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule resolution :premises (t826 t827))
% 6.76/7.01  (step t829 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (not (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t830 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule resolution :premises (t828 t829))
% 6.76/7.01  (step t831 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y)))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c))))) :rule contraction :premises (t830))
% 6.76/7.01  (step t832 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.inverse (tptp.greatest_lower_bound X Y)) (tptp.least_upper_bound (tptp.inverse X) (tptp.inverse Y))))) (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule implies :premises (t831))
% 6.76/7.01  (step t833 (cl (= (tptp.inverse (tptp.greatest_lower_bound tptp.a tptp.c)) (tptp.least_upper_bound (tptp.inverse tptp.a) (tptp.inverse tptp.c)))) :rule resolution :premises (t832 a20))
% 6.76/7.01  (step t834 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t835)
% 6.76/7.01  (assume t835.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))
% 6.76/7.01  (step t835.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.c)))
% 6.76/7.01  (step t835.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule or :premises (t835.t1))
% 6.76/7.01  (step t835.t3 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule resolution :premises (t835.t2 t835.a0))
% 6.76/7.01  (step t835 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule subproof :discharge (t835.a0))
% 6.76/7.01  (step t836 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule resolution :premises (t834 t835))
% 6.76/7.01  (step t837 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (not (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))))) :rule implies_neg2)
% 6.76/7.01  (step t838 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))))) :rule resolution :premises (t836 t837))
% 6.76/7.01  (step t839 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c))))) :rule contraction :premises (t838))
% 6.76/7.01  (step t840 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule implies :premises (t839))
% 6.76/7.01  (step t841 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X))) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule equiv_pos2)
% 6.76/7.01  (anchor :step t842 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 6.76/7.01  (step t842.t1 (cl (= X X)) :rule refl)
% 6.76/7.01  (step t842.t2 (cl (= Y Y)) :rule refl)
% 6.76/7.01  (step t842.t3 (cl (= (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule all_simplify)
% 6.76/7.01  (step t842 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)) X)) (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y)))))) :rule bind)
% 6.76/7.01  (step t843 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= X (tptp.greatest_lower_bound X (tptp.least_upper_bound X Y))))) :rule resolution :premises (t841 t842 a10))
% 6.76/7.01  (step t844 (cl (= tptp.a (tptp.greatest_lower_bound tptp.a (tptp.least_upper_bound tptp.a tptp.c)))) :rule resolution :premises (t840 t843))
% 6.76/7.01  (step t845 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t846)
% 6.76/7.01  (assume t846.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))))
% 6.76/7.01  (step t846.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.c)))
% 6.76/7.01  (step t846.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule or :premises (t846.t1))
% 6.76/7.01  (step t846.t3 (cl (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule resolution :premises (t846.t2 t846.a0))
% 6.76/7.01  (step t846 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule subproof :discharge (t846.a0))
% 6.76/7.01  (step t847 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule resolution :premises (t845 t846))
% 6.76/7.01  (step t848 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (not (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) :rule implies_neg2)
% 6.76/7.01  (step t849 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) :rule resolution :premises (t847 t848))
% 6.76/7.01  (step t850 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a)))) :rule contraction :premises (t849))
% 6.76/7.01  (step t851 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.least_upper_bound X Y) (tptp.least_upper_bound Y X)))) (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule implies :premises (t850))
% 6.76/7.01  (step t852 (cl (= (tptp.least_upper_bound tptp.a tptp.c) (tptp.least_upper_bound tptp.c tptp.a))) :rule resolution :premises (t851 a4))
% 6.76/7.01  (step t853 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t854)
% 6.76/7.01  (assume t854.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))))
% 6.76/7.01  (step t854.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.c)))
% 6.76/7.01  (step t854.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule or :premises (t854.t1))
% 6.76/7.01  (step t854.t3 (cl (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule resolution :premises (t854.t2 t854.a0))
% 6.76/7.01  (step t854 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule subproof :discharge (t854.a0))
% 6.76/7.01  (step t855 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule resolution :premises (t853 t854))
% 6.76/7.01  (step t856 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (not (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule implies_neg2)
% 6.76/7.01  (step t857 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule resolution :premises (t855 t856))
% 6.76/7.01  (step t858 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a)))) :rule contraction :premises (t857))
% 6.76/7.01  (step t859 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.greatest_lower_bound X Y) (tptp.greatest_lower_bound Y X)))) (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule implies :premises (t858))
% 6.76/7.01  (step t860 (cl (= (tptp.greatest_lower_bound tptp.a tptp.c) (tptp.greatest_lower_bound tptp.c tptp.a))) :rule resolution :premises (t859 a3))
% 6.76/7.01  (step t861 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) :rule implies_neg1)
% 6.76/7.01  (anchor :step t862)
% 6.76/7.01  (assume t862.a0 (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))))
% 6.76/7.01  (step t862.t1 (cl (or (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))) :rule forall_inst :args ((:= X tptp.identity)))
% 6.76/7.01  (step t862.t2 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule or :premises (t862.t1))
% 6.76/7.01  (step t862.t3 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule resolution :premises (t862.t2 t862.a0))
% 6.76/7.01  (step t862 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule subproof :discharge (t862.a0))
% 6.76/7.01  (step t863 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule resolution :premises (t861 t862))
% 6.76/7.01  (step t864 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (not (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))) :rule implies_neg2)
% 6.76/7.01  (step t865 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))) :rule resolution :premises (t863 t864))
% 6.76/7.01  (step t866 (cl (=> (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity)))) :rule contraction :premises (t865))
% 6.76/7.01  (step t867 (cl (not (forall ((X $$unsorted)) (= tptp.identity (tptp.multiply (tptp.inverse X) X)))) (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule implies :premises (t866))
% 6.76/7.01  (step t868 (cl (= tptp.identity (tptp.multiply (tptp.inverse tptp.identity) tptp.identity))) :rule resolution :premises (t867 t677))
% 6.76/7.01  (step t869 (cl (= tptp.identity (tptp.inverse tptp.identity))) :rule symm :premises (a15))
% 6.76/7.01  (step t870 (cl) :rule resolution :premises (t109 t117 t125 t133 t141 t149 t157 t168 t176 t184 t192 t200 t208 t216 t224 t232 t240 t248 t256 t267 t275 t283 t291 t299 t307 t315 t323 t331 t339 t347 t355 t363 t371 t379 t387 t395 t403 t411 t419 t427 t435 t443 t451 t459 t467 t475 t483 t491 t499 t507 t515 t523 t531 t539 t547 t555 t563 t571 t579 t587 t595 t603 t611 t619 t627 t635 t643 t651 t659 t667 t678 t686 t694 t702 t710 t718 t729 t737 t745 t753 t761 t769 t777 t785 t793 t801 t809 t817 t825 t833 t844 t852 t860 t868 a22 a19 a18 t869))
% 6.76/7.01  
% 6.80/7.04  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.oh4OzLmSnw/cvc5---1.0.5_1497.smt2
% 6.80/7.05  % cvc5---1.0.5 exiting
% 6.80/7.05  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------